Question

8 which expression is equivalent to $4^{7} \times 4^{-5}$? a $4^{12}$ b $4^{-35}$ c $4^{2}$ d $4^{-2}$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying exponents with the same base, we use the rule \(a^m \times a^n = a^{m + n}\). Here, the base \(a = 4\), \(m = 7\), and \(n=- 9\) (assuming the second exponent is \(-9\) as there seems to be a typo, likely \(4^{-9}\) instead of \(4^{-b}\)).
So, \(4^{7}\times4^{-9}=4^{7+( - 9)}\)

Step2: Calculate the exponent

Calculate \(7+( - 9)=7 - 9=-2\). So the expression is equivalent to \(4^{-2}\)

Answer:

D. \(4^{-2}\)