Simplify each expression, but don’t evaluate.
${\left(4^{15}\right)}^3$

• A. $4^{18}$
• B. $4^5$
• C. $4^{12}$
• D. $4^{45}$

Answer: (D)

Verified step by step guidance

1. Identify the expression to simplify: \(\left(4^{15}\right)^3\).
2. Recall the power of a power rule: \((a^m)^n = a^{m \times n}\).
3. Apply the rule by multiplying the exponents: \(15 \times 3\).
4. Rewrite the expression as a single power: \(4^{15 \times 3}\).
5. Express the simplified form as \$4^{45}$ without calculating the numerical value.