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Operations with rational exponents

Factor completely.

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-2 x^{4}-20 x^{3}-18 x^{2}

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Factor completely.

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3 x^{3}-39 x^{2}+36 x

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Factor the expression completely.

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x^{4}+7 x^{2}-18

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Factor the expression completely.

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x^{4}-7 x^{2}-18

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Factor the expression completely.

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x^{4}-10 x^{2}+9

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Factor the expression completely.

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x^{4}+8 x^{2}-9

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Factor the expression completely.

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x^{4}-4 x^{2}-12

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Factor completely.

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4 x^{4}-48 x^{3}+128 x^{2}

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Factor completely.

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5 x^{3}+55 x^{2}+120 x

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Factor the expression completely.

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10 x^{5}-7 x^{2}

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\frac{2}{10} \div \frac{1}{7}

\frac{8^{4}}{{4^{8}}}

-4x^{2}+7=12x

is rewritten in the form of

-4(x-p)^{2}+q=0

. What is the value of

q

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-2

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\frac{19}{4}

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\frac{37}{4}

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16

-4x^{2}+7=12x

is rewritten in the form of

-4(x-p)^{2}+q=0

. What is the value of

q

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-2

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\frac{19}{4}

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\frac{37}{4}

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16

(16^{\frac{5}{9}} \cdot 5^{\frac{7}{9}})^{-3}

[(9f+9)+(9f+9+1)]\cdot f

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

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1

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18(f^{2}+f)

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18f^{2}+18f+1

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18(f^{2}+f+1)

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18f^{2}+19f

Which expression is equivalent to

\frac{\left(3^{4}\right)^{-6}}{3^{-5}} ?

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3^{-29}

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3^{-19}

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3^{19}

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3^{-21}

Which expression is equivalent to

\left(4 \times 4^{-1}\right)^{3}

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16

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1

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\frac{1}{64}

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0

Which expression is equivalent to

\left(\frac{2}{2^{5}}\right)^{-1} ?

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16

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32

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64

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\frac{1}{32}

Which expression is equivalent to

4^{-4} \times \frac{4^{-2}}{4^{2}} ?

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4^{16}

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16^{16}

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16^{-8}

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4^{-8}

Which expression is equivalent to

\frac{2^{-5}}{2^{-3}} \times 2^{-4}

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2^{2}

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2^{-6}

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2^{-7}

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2^{-2}

Which set of ordered pairs

(x, y)

could represent a linear function?

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\begin{array}{l} \mathbf{A}=\{(-1,0),(2,3),(5,6),(9,9)\} \\ \mathbf{B}=\{(-2,9),(-1,6),(1,3),(3,0)\} \\ \mathbf{C}=\{(0,5),(3,2),(6,-1),(9,-4)\} \\ \mathbf{D}=\{(3,-8),(5,-4),(7,-1),(9,2)\} \end{array}

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Which set of ordered pairs

(x, y)

could represent a linear function?

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\begin{array}{l} \mathbf{A}=\{(-4,0),(-1,3),(2,6),(5,8)\} \\ \mathbf{B}=\{(0,5),(3,2),(6,-1),(9,-5)\} \\ \mathbf{C}=\{(-1,7),(0,5),(2,1),(3,-1)\} \\ \mathbf{D}=\{(-9,-7),(-3,-4),(2,-1),(8,2)\} \end{array}

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x

satisfies the equation

\frac{5}{4}\left(x-\frac{2}{3}\right)=\frac{125}{12}

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8

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-9

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-8

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9

x

satisfies the equation

\frac{2}{3}\left(x-\frac{5}{6}\right)=-\frac{59}{9}

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9

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-9

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-8

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8

Simplify to a single power of

6

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\frac{6^{7}}{6^{5}}

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6 ^\square

For the following equation, find

f^{\prime}(x)

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f(x)=7 x^{4}-6 x^{2}-1

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f^{\prime}(x)=

Perform the operation and simplify the answer fully.

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\frac{10}{7} \cdot \frac{1}{2}

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Perform the operation and simplify the answer fully.

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\frac{4}{3} \div \frac{4}{5}

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Perform the operation and simplify the answer fully.

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\frac{1}{2} \div \frac{5}{6}

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\frac{25 \times 5^{2} \times t^{8}}{10^{3} \times t^{4}}

Perform the operation and simplify the answer fully.

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\frac{1}{2} \div \frac{6}{5}

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Perform the operation and simplify the answer fully.

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\frac{1}{2} \div \frac{7}{5}

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Perform the operation and simplify the answer fully.

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\frac{8}{9} \div \frac{7}{6}

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\log_{9}\left(\frac{x^{3}}{16}\right)

\log\left(\frac{64}{9}\right)

Solve the equation.

\begin{align*} \left(\frac{a}{7}\right) &= 9,\ a &= \Box \end{align*}

\left(10x^{3}-5x^{2}-6x\right)\div\left(2x^{2}\right)

y=\cos^{4}x\sin^{4}x

g(x)=x^{\frac{4}{3}}

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g^{\prime}(27)=

What is the value of

\frac{d}{d x}\left(x^{\frac{5}{4}}\right)

x=16

h(x)=x^{\frac{5}{2}}

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h^{\prime}(x)=

f(x)=x^{-1}

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f^{\prime}(x)=

What is the area of the region between the graphs of

f(x)=x^{2}-3 x

g(x)=2 x

x=0

x=5

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1

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\frac{175}{6}

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25

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\frac{325}{6}

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\frac{125}{6}

What is the area of the region bound by the graphs of

f(x)=\sqrt{x-2}, g(x)=14-x

x=2

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1

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\frac{99}{2}

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\frac{19}{6}

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\frac{151}{2}

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\frac{45}{2}

What is the area of the region bound by the graphs of

f(x)=\sqrt{x-2}, g(x)=14-x

x=2

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1

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\frac{19}{6}

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\frac{99}{2}

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\frac{151}{2}

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\frac{45}{2}

What is the area of the region between the graphs of

f(x)=x^{2}-4 x+1

g(x)=3 x-5

x=1

x=4

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1

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\frac{125}{6}

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\frac{27}{2}

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4

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\frac{81}{2}

What is the area of the region bound by the graphs of

f(x)=-x^{2}, g(x)=3 x-10

x=0

in quadrant IV?

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1

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2

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\frac{8}{3}

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\frac{16}{3}

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\frac{34}{3}

Last week, the thickness of the ice on a lake increased by

\frac{25}{t+3}

centimeters per day (where

t

is the number of days since the ice first formed).

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By how many centimeters did the thickness of the ice increase between

t=0

t=4

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1

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\frac{1,000}{441}

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\frac{100}{21}

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25 \ln \left(\frac{7}{3}\right)

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25 \ln (4)

f(x)=2 \cos \left(\frac{x}{2}\right)

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f^{\prime \prime}(x)

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1

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-\cos \left(\frac{x}{2}\right)

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-\sin \left(\frac{x}{2}\right)

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-8 \cos \left(\frac{x}{2}\right)

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-\frac{1}{2} \cos \left(\frac{x}{2}\right)

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