Question

which expression is equivalent to (left( \frac{5^{3}}{5^{-3}}
ight)^{3})?
answer
(5^{9}) (quad) (5^{24})
(5^{-3}) (quad) (5^{18})

Explanation:

Step1: Simplify the fraction inside the parentheses using exponent rules (when dividing with the same base, subtract exponents: \( \frac{a^m}{a^n} = a^{m - n} \))

\( \frac{5^3}{5^{-3}} = 5^{3 - (-3)} = 5^{3 + 3} = 5^6 \)

Step2: Apply the power of a power rule (multiply exponents: \( (a^m)^n = a^{m \times n} \)) to the result from Step1

\( (5^6)^3 = 5^{6 \times 3} = 5^{18} \)

Answer:

\( 5^{18} \) (the option corresponding to \( 5^{18} \))