Question

Simplify the expression. The simplified expression should have no negative exponents. $$ \left(\frac{1}{x}\right)^{5} $$

Short answer

The simplified expression is \( \frac{1}{x^{5}} \)

Step-by-step solution

Write down the expression

Write down the expression as it is \( \left(\frac{1}{x}\right)^{5} \).

Apply the exponent rule

In the given expression, x is in the denominator with an implied exponent of -1. This exponent needs to be multiplied with the given exponent which is 5. Hence, use the rule am.n = a^(m*n). So the expression becomes \( x^{-5} \).

Simplify the expression

The result obtained in Step 2 is \( x^{-5} \). We need to convert this negative exponent to a positive exponent. The rule to convert negative exponent to positive is a^(-n) = 1/a^n. Applying this rule, the answer simplifies to \( \frac{1}{x^{5}} \).