Question

select the equivalent expression.
\\(\frac{x^{-7} \cdot x^{8}}{x^{8}}\\)
answer attempt 1 out of 3
\\(x^8\\) \\(\frac{1}{x^7}\\) \\(\frac{1}{x^8}\\) \\(x^7\\)

Explanation:

Step1: Simplify numerator (product rule)

When multiplying exponents with the same base, add exponents: $x^a \cdot x^b = x^{a+b}$
$x^{-7} \cdot x^8 = x^{-7+8} = x^{1} = x$

Step2: Simplify the fraction (quotient rule)

When dividing exponents with the same base, subtract exponents: $\frac{x^a}{x^b} = x^{a-b}$
$\frac{x}{x^8} = x^{1-8} = x^{-7}$

Step3: Rewrite negative exponent

A negative exponent means reciprocal: $x^{-a} = \frac{1}{x^a}$
$x^{-7} = \frac{1}{x^7}$

Answer:

$\frac{1}{x^7}$