Question

select the equivalent expression.
\frac{x^{-8}x^{-7}y^{5}y^{-7}}{1}
answer attempt 1 out of 3
\circ x^{15}y^{2} \circ \frac{y^{2}}{x} \circ \frac{1}{x^{15}y^{2}} \circ \frac{x}{y^{2}}

Explanation:

Step1: Combine like x-terms

When multiplying terms with the same base, add exponents: $x^{-8}x^{-7}=x^{-8+(-7)}=x^{-15}$

Step2: Combine like y-terms

Apply exponent rule to y-terms: $y^{5}y^{-7}=y^{5+(-7)}=y^{-2}$

Step3: Rewrite negative exponents

Use $a^{-n}=\frac{1}{a^n}$: $x^{-15}y^{-2}=\frac{1}{x^{15}y^{2}}$

Answer:

$\frac{1}{x^{15}y^{2}}$