Question

simplify ((4^{3})^{5}).
a. (left(\frac{1}{4}
ight)^{15})
b. (4^{15})
c. (12^{5})
d. (4^{8})

Explanation:

Step1: Recall the power of a power rule

The power of a power rule states that \((a^m)^n = a^{m\times n}\), where \(a\) is the base and \(m\) and \(n\) are exponents.

Step2: Apply the rule to \((4^3)^5\)

Here, \(a = 4\), \(m = 3\), and \(n = 5\). Using the power of a power rule, we multiply the exponents: \(3\times5 = 15\). So, \((4^3)^5 = 4^{3\times5}=4^{15}\).

Answer:

B. \(4^{15}\)