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. The Power Rule for Exponents states that when you raise a power to another power, you multiply the exponents. In mathematical terms, this is written as \(\left(a^{m}\right)^{n} = a^{m \times n}\).
2. Identify the base and the exponents in the given expression. For example, if you have \(\left(x^{3}\right)^{4}\), the base is \(x\), the first exponent is 3, and the second exponent is 4.
3. Apply the Power Rule by multiplying the exponents together. Using the example, multiply 3 and 4 to get \$3 \times 4 = 12$.
4. Rewrite the expression with the base and the new exponent. So, \(\left(x^{3}\right)^{4}\) becomes \(x^{12}\) after applying the rule.
5. Remember that this rule only applies when the base is the same and you are raising a power to another power. If there are different bases or other operations, use the appropriate exponent rules.