Question

simplify the expression using exponent rules. leave your answer in exponential form with a positive exponent. (1 point)
$(a^{2} \times a^{-5})^{2} = \square$

Explanation:

Step1: Add exponents inside parentheses

When multiplying like bases, add exponents: $a^m \times a^n = a^{m+n}$.
$a^{2 + (-5)} = a^{-3}$

Step2: Apply power of a power rule

Raise the result to the 2nd power: $(a^m)^n = a^{m \times n}$.
$(a^{-3})^2 = a^{-3 \times 2} = a^{-6}$

Step3: Convert to positive exponent

Use the rule $a^{-n} = \frac{1}{a^n}$.
$a^{-6} = \frac{1}{a^6}$

Answer:

$\frac{1}{a^6}$