Question

which expression is equivalent to \\((4^{-3})^{-6}\\)?

\\(4^{18}\\)

\\(4^{-18}\\)

\\(4^{3}\\)

\\(4^{-9}\\)

Explanation:

Step1: Identify the exponent rule

Apply the power of a power rule: \((a^m)^n = a^{m \cdot n}\).

$$(4^{-3})^{-6} = 4^{-3 \cdot (-6)}$$

Step2: Multiply the exponents

Multiply the negative integers to find the final exponent.

$$-3 \cdot (-6) = 18$$

Step3: Write the final expression

Simplify the expression with the new exponent.

$$4^{18}$$

Answer:

\(4^{18}\)