Compute the exact value of the function for the given x-value without using a calculator.
-$$f ( x ) = 3 \cdot 25 ^ { x } \text { for } x = - 3 / 2$$
A) 45
B) 375
C) $\frac { 3 } { 125 }$
D) $- \frac { 3 } { 125 }$

Question

Quizplus · Accepted Answer

$$f(x) = 3 \cdot 25^x = 3 \cdot 25^{-3/2} = 3 \cdot (25^{-1})^{3/2} = 3 \cdot \left(\frac{1}{25}\right)^{3/2} = 3 \cdot \left(\frac{1}{5^2}\right)^{3/2} = 3 \cdot \frac{1}{5^3} = \frac{3}{125}$$

Compute the Exact Value of the Function for the Given f(x)=3⋅25x for x=−3/2f ( x ) = 3 \cdot 25 ^ { x } \text { for } x = - 3 / 2f(x)=3⋅25x for x=−3/2

Compute the Exact Value of the Function for the Given $f ( x ) = 3 \cdot 25 ^ { x } \text { for } x = - 3 / 2$