Question

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

answer
\\(4^3\\) \\(4^6\\)
\\(4^{-1}\\) \\(4^{-9}\\)

Explanation:

Step1: Apply exponent division rule

When dividing exponents with the same base, subtract the denominator exponent from the numerator exponent: $a^m / a^n = a^{m-n}$
$\frac{4^3}{4^{-3}} = 4^{3 - (-3)}$

Step2: Simplify the exponent

Calculate the value of the exponent:
$4^{3 + 3} = 4^6$

Answer:

$4^6$