Question

determine whether each expression is equivalent to $15^{-4}$. equivalent to $15^{-4}$ not equivalent to $15^{-4}$ $\frac{15^{-6}}{15^{-1}}$

Explanation:

Step1: Apply exponent quotient rule

When dividing terms with the same base, subtract exponents: $\frac{a^m}{a^n}=a^{m-n}$
$\frac{15^{-6}}{15^{-1}}=15^{-6-(-1)}$

Step2: Simplify the exponent

Calculate the subtraction in the exponent.
$15^{-6+1}=15^{-5}$

Step3: Compare to target expression

$15^{-5}
eq 15^{-4}$

Answer:

$\frac{15^{-6}}{15^{-1}}$ is Not Equivalent to $15^{-4}$