Question

simplify the following expression:
$xy^{-7}$
options: $x^7y$, $\frac{x}{y^7}$, $xy^7$, $\frac{x^7}{y}$

Explanation:

Step1: Recall the negative exponent rule

The rule for negative exponents is \( a^{-n} = \frac{1}{a^n} \) (where \( a
eq 0 \) and \( n \) is a positive integer). For the term \( y^{-7} \), we can apply this rule.

Step2: Apply the rule to the expression

Given the expression \( xy^{-7} \), we apply the negative exponent rule to \( y^{-7} \). So \( y^{-7} = \frac{1}{y^7} \). Then the expression \( xy^{-7} \) becomes \( x\times\frac{1}{y^7} \), which simplifies to \( \frac{x}{y^7} \).

Answer:

\(\frac{x}{y^7}\) (corresponding to the option "x/y⁷")