Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

2^(5)*((1)/(4))^(7) Which of the following expressions is equivalent to the given expression? Choose 1 answer: (A) 2^(-2) (B) 2^(-4) (c) 2^(-9) (D) 2^(10)

25⋅(14)7 2^{5} \cdot\left(\frac{1}{4}\right)^{7} \newlineWhich of the following expressions is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) 2−2 2^{-2} \newline(B) 2−4 2^{-4} \newline(C) 2−9 2^{-9} \newline(D) 210 2^{10}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear and exponential growthright chevron icon

Full solution

Q. 25⋅(14)7 2^{5} \cdot\left(\frac{1}{4}\right)^{7} \newlineWhich of the following expressions is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) 2−2 2^{-2} \newline(B) 2−4 2^{-4} \newline(C) 2−9 2^{-9} \newline(D) 210 2^{10}
  1. Understand Expression: Understand the given expression and the properties of exponents.\newlineWe have the expression 25×(14)72^{5}\times\left(\frac{1}{4}\right)^{7}. We know that (14)\left(\frac{1}{4}\right) is the same as 2−22^{-2} because 14=222=2122=2(1−2)=2−1\frac{1}{4} = \frac{2}{2^2} = \frac{2^1}{2^2} = 2^{(1-2)} = 2^{-1}.
  2. Rewrite Using Property: Rewrite the expression using the property from Step 11.\newlineWe can rewrite (14)7\left(\frac{1}{4}\right)^{7} as (2−2)7(2^{-2})^{7}.\newlineSo, the expression becomes 25⋅(2−2)7.2^{5} \cdot (2^{-2})^{7}.
  3. Apply Power Rule: Apply the power of a power rule to the second term.\newlineUsing the power of a power rule (am)n=am∗n(a^{m})^{n} = a^{m*n}, we get:\newline(2−2)7=2−2∗7=2−14(2^{-2})^{7} = 2^{-2*7} = 2^{-14}.\newlineNow, the expression is 25×2−142^{5} \times 2^{-14}.
  4. Combine Terms: Apply the product of powers rule to combine the terms.\newlineUsing the product of powers rule am×an=a(m+n)a^m \times a^n = a^{(m+n)}, we combine the terms:\newline25×2−14=2(5−14)=2−9.2^{5} \times 2^{-14} = 2^{(5-14)} = 2^{-9}.
  5. Match with Options: Match the result with the given options.\newlineThe simplified expression is 2−92^{-9}, which matches option (C)(C).

More problems from Compare linear and exponential growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 8 months ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 8 months ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 8 months ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 9 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 8 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 9 months ago

View all (345)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant