Evaluate the Function f(x)=(1.25^(x/4))^16

$f (x) = {({1.25}^{\frac{x}{4}})}^{16}$

Step 1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f (x) = {1.25}^{\frac{x}{4} \cdot 16}$

Step 2

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$f (x) = {1.25}^{\frac{x}{4} \cdot (4 (4))}$

Cancel the common factor.

$f (x) = {1.25}^{\frac{x}{4} \cdot (4 \cdot 4)}$

Rewrite the expression.

$f (x) = {1.25}^{x \cdot 4}$

Step 3

Move $4$ to the left of $x$ .

$f (x) = {1.25}^{4 x}$

Step 4