Write as an Equation f(x)=(1.25^(x/4))^16

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

Rewrite the function as an equation.

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

Multiply the exponents in ${({1.25}^{\frac{x}{4}})}^{16}$ .

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

$y = {1.25}^{\frac{x}{4} \cdot 16}$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = {1.25}^{x \cdot 4}$

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

$y = {1.25}^{4 x}$