Question

1. $(x^{-2})^{-7} =$

a $x^5$
b $x^{14}$
c $\frac{1}{x^5}$
d $\frac{1}{x^{14}}$

Explanation:

Step1: Recall the power of a power rule

The power of a power rule states that \((a^m)^n = a^{m \times n}\). Here, \(a = x\), \(m = -2\), and \(n = -7\).

Step2: Apply the power of a power rule

Using the rule \((x^{-2})^{-7}\), we multiply the exponents: \(-2 \times -7 = 14\). So, \((x^{-2})^{-7}=x^{14}\).

Answer:

B. \(X^{14}\)