Algebra Examples

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

Step 1

Rewrite the function as an equation.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factor of $4$ .

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Step 2.2.1

Factor $4$ out of $16$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.3

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

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