Question

15/37 \\(\frac{x^5}{x^{-2}}\\) \\(x^3\\) \\(\frac{1}{x^3}\\) \\(x^7\\) \\(\frac{1}{x^7}\\)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we subtract the exponents: \( \frac{x^m}{x^n}=x^{m - n} \). But wait, the given expression is \( \frac{x^5}{x^{-2}} \) (assuming a typo, because \( x - 2 \) as denominator would not match the options; likely \( x^{-2} \)). So applying the rule \( \frac{x^5}{x^{-2}}=x^{5-(-2)} \).

Step2: Simplify the exponent

Calculate \( 5-(-2)=5 + 2 = 7 \), so \( x^{5-(-2)}=x^7 \).

Answer:

\( x^7 \) (corresponding to the orange option with \( x^7 \))