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Multiplication with rational exponents

\frac{d}{d w}\left(2 w^{2}+4 \cos w\right)

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\frac{d}{d v}\left(5 v^{3}+5 \sin v\right)

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\frac{d}{d g}\left(g^{4}+3 \sin g\right)

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Simplify. Write your answer as a proper or improper fraction in simplest form.

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\frac{\frac{5}{8}} {\frac{5}{8}}=\frac{\Box}{\Box}

Select the equivalent expression.

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\left(\frac{b^{7}}{4^{5}}\right)^{-3}=

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1

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\frac{b^{21}}{4^{15}}

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\frac{4^{15}}{b^{21}}

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b^{-21}\cdot 4^{-15}

Select the equivalent expression.

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\left(\frac{b^{7}}{4^{5}}\right)^{-3}=

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1

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b^{-21}\cdot4^{-15}

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\frac{b^{21}}{4^{15}}

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\frac{4^{15}}{b^{21}}

Which of the following is equivalent to

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\frac{\log_{c}(6)}{\log(6)}

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1

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\log(c)

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\log_{c}(1)

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\frac{1}{\log(c)}

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\frac{1}{\log(6)}

Which of the following is equivalent to

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\log_{4}(m)\cdot\log_{m}(20)

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1

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5

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80

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\log(5)

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\log_{4}(20)

4

glue sticks cost

\$7.76

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Which equation would help determine the cost of

13

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1

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\frac{x}{13} = \frac{4}{\$7.76}

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\frac{13}{x} = \frac{\$7.76}{4}

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\frac{4}{\$7.76} = \frac{13}{x}

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\frac{13}{4} = \frac{\$7.76}{x}

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(E) None of the above

Percy and Jim are calling their customers. Percy has called

\frac{9}{10}

of his customers. Jim has called

\frac{1}{9}

of his customers. Who has called a greater fraction of his customers?

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\frac{d}{dx}(x \cdot 2^{x})

Which expression is equivalent to

10-8

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1

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8-10

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10-(-8)

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10+(-8)

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-8-10

What is the sign of

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-\frac{88}{13}+\frac{88}{13}

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1

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(C) Neither positive nor negative-the sum is zero.

Which expression is equivalent to

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11-(-\frac{3(5)}{8})

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1

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11+\frac{3(5)}{8}

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\frac{3(5)}{8}+(-11)

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11+(-\frac{3(5)}{8})

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-\frac{3(5)}{8}-11

Which expression is equivalent to

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-9-(-4\frac{1}{3})

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1

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-9+4\frac{1}{3}

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-4\frac{1}{3}-(-9)

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-4\frac{1}{3}+(-9)

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9-(-4\frac{1}{3})

Which expressions are equivalent to

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\sqrt[5]{b^{9}}

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Choose all answers that apply:

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b^{\left(\frac{9}{5}\right)}

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b^{\left(\frac{5}{9}\right)}

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(b^{5})^{\left(\frac{1}{9}\right)}

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D None of the above

Which expression is equivalent to

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4.25-(-8)

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1

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-8+(-4.25)

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4.25+(-8)

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4.25+8

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8-4.25

Which expressions are equivalent to

\sqrt[5]{b^{9}}

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Choose all answers that apply:

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b^{\frac{9}{5}}

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b^{\frac{5}{9}}

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(b^{5})^{\frac{1}{9}}

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(D) None of the above

Which expression is equivalent to

4.25-(-8)

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1

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-8+(-4.25)

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4.25+(-8)

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4.25+8

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8-4.25

Which exponential expression is equivalent to

\sqrt[4]{x^3}

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1

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\frac{x^3}{x^4}

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x^{\frac{4}{3}}

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x^{\frac{3}{4}}

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\frac{x^4}{x^3}

Which exponential expression is equivalent to

\sqrt{k}

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1

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\frac{1}{k^{2}}

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\frac{1}{k^{\frac{1}{2}}}

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k^{2}

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k^{\frac{1}{2}}

Solve the equation.

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10=\frac{p}{10}

p=\Box

Solve the equation.

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9 = \frac{h}{9}

h = \Box

\left(\frac{6}{8}\right)\times\left(\frac{7}{8}\right)

\left(-2 j^{2}\right) \cdot\left(\frac{1}{4}\right)+\left(\frac{1}{2} j^{2}-1\right)

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Which of the following expressions is equivalent to the given expression?

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1

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-1

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\frac{3}{8} j^{2}-1

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\left(\frac{j}{2}+1\right)\left(\frac{j}{2}-1\right)

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(j+1)(j-1)

f(t)=20\left(\frac{1}{8}\right)^{t}

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Which of the following is an equivalent form of the function

f

in which the base of the exponent is

\frac{1}{2}

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1

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f(t)=5\left(\frac{1}{2}\right)^{t}

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f(t)=20\left(\frac{1}{2}\right)^{\frac{t}{4}}

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f(t)=20\left(\frac{1}{2}\right)^{3 t}

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f(t)=20\left(\frac{1}{2}\right)^{4 t}

f(t)=1,000\left(\frac{1}{16}\right)^{\frac{t}{4}}

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Which of the following is an equivalent form of the function

f

in which the base of the exponent is

\frac{1}{2}

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1

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f(t)=125\left(\frac{1}{2}\right)^{\frac{t}{4}}

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f(t)=1,000\left(\frac{1}{2}\right)^{t}

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f(t)=1,000\left(\frac{1}{2}\right)^{2 t}

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f(t)=1,000\left(\frac{1}{2}\right)^{4 t}

(z^{-(1)/(3)})/(z^{-(5)/(6)})=

\ln\left(\frac{1}{x}\right)+\ln(2x^{3})=\ln 3

\frac{1}{3}+\frac{2}{2}

\frac{3}{4}-\frac{3}{8}

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f(x)=(2x-1)(3x+7)

is graphed in the

xy

-plane. Which of the following are the coordinates of an

x

-intercept of the graph?

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1

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\left(-\frac{3}{7},0\right)

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\left(\frac{1}{2},0\right)

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(2,0)

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\left(\frac{7}{3},0\right)

Given the function

f(x)=(x+8)\left(3 x+5-3 x^{2}\right)

f^{\prime}(x)

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f^{\prime}(x)=

Given the function

y=\left(10 x^{-1}+10+8 x^{-3}\right)\left(9 x^{2}-5\right)

\frac{d y}{d x}

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\frac{d y}{d x}=

\frac{d}{d x}(-\sin (4 x+1))

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\frac{d}{d x}(-7 \sin (-x))

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\frac{d}{d x}(-4 \sin x)

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\frac{d}{d x}(-7 \cos x+2)

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\frac{d}{d x}(-3 \sin x)

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\frac{d}{d x}(-5 \cos (7 x-1))

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Given the function

y=\left(-4+5 x^{-3}+7 x^{-2}\right)\left(-2-5 x^{-1}\right)

\frac{d y}{d x}

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\frac{d y}{d x}=

What is the value of

\frac{d}{d x}\left(\sqrt[5]{x^{2}}\right)

x=32

f(x)=\frac{1}{x^{7}}

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f^{\prime}(x)=

g(x)=x^{\frac{1}{4}}

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g^{\prime}(x)=

What is the value of

\frac{d}{d x}\left(x^{-6}\right)

x=1

h(x)=x^{\frac{1}{4}}

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h^{\prime}(16)=

f(x)=x^{\frac{1}{2}}

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f^{\prime}(4)=

What is the value of

\frac{d}{d x}\left(\frac{1}{x^{4}}\right)

x=2

h(x)=\frac{1}{x^{6}}

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h^{\prime}(1)=

What is the value of

\frac{d}{d x}\left(\frac{1}{x^{5}}\right)

x=2

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