Which of these expressions is equivalent to ?
A. 1
OB.
C.
(O. .

Ask by Macdonald Paul. in the United States

Mar 25,2025

Question

Which of these expressions is equivalent to $$ \left(5^{3}\right)^{-2}\left(5^{2}\right)^{3} $$ ? A. 1 OB. $$ 5^{6} $$ C. $$ -5^{5} $$ (O. $$ \frac{1}{56} $$.

UpStudy AI · Accepted Answer

1. Rewrite each expression using the exponent rule $$ (a^b)^c = a^{bc} $$:
   - $$ \left(5^{3}\right)^{-2} = 5^{3 \cdot (-2)} = 5^{-6} $$
   - $$ \left(5^{2}\right)^{3} = 5^{2 \cdot 3} = 5^{6} $$

2. Multiply the two results using the law $$ a^m \cdot a^n = a^{m+n} $$:
   $$
   5^{-6} \cdot 5^6 = 5^{-6+6} = 5^0
   $$

3. Recall that any nonzero number raised to the power 0 is 1:
   $$
   5^0 = 1
   $$

The equivalent expression is $$ 1 $$, which corresponds to option A.
The equivalent expression is 1, which is option A.

Which of these expressions is equivalent to ?
A. 1
OB.
C.
(O. .

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Which of these expressions is equivalent to ? A. 1 OB. C. (O. .