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Which of the following is equal to $8^5$ ?
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23 Sep 2025, 01:12
23 Sep 2025, 01:12
Expert Reply
00:00
Question Stats:
50% (00:48) correct
50% (00:38) wrong based on 2 sessions
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Which of the following is equal to $\(8^5\)$ ?
Indicate all correct expressions.
(A) $\(2^5 \times 4^5\)$
(B) $\(2^{15}\)$
(C) $\(2 \times 4^7\)$
Indicate all correct expressions.
(A) $\(2^5 \times 4^5\)$
(B) $\(2^{15}\)$
(C) $\(2 \times 4^7\)$
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Re: Which of the following is equal to $8^5$ ?
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16 Oct 2025, 12:43
16 Oct 2025, 12:43
Expert Reply
Let's analyze each option for equality with $\(8^5\)$ :
Step 1: Express $\(8^5\)$ in terms of base 2 :
Since $\(8=2^3\)$,
$$
\(8^5=\left(2^3\right)^5=2^{3 \times 5}=2^{15}\)
$$
Step 2: Check each option
- (A) $\(2^5 \times 4^5\)$
Since $\(4=2^2\)$, this becomes:
$$
\(2^5 \times\left(2^2\right)^5=2^5 \times 2^{10}=2^{15}\)
$$
Equal to $\(8^5\)$.
- (B) $\(2^{15}\)$
Directly matches $\(8^5\)$.
- (C) $\(2 \times 4^7\)$
Since $\(4=2^2\)$, this becomes:
$$
\(2 \times\left(2^2\right)^7=2 \times 2^{14}=2^{15}\)
$$
Equal to $\(8^5\)$.
Conclusion:
All three expressions (A), (B), and (C) equal $\(8^5\)$.
Step 1: Express $\(8^5\)$ in terms of base 2 :
Since $\(8=2^3\)$,
$$
\(8^5=\left(2^3\right)^5=2^{3 \times 5}=2^{15}\)
$$
Step 2: Check each option
- (A) $\(2^5 \times 4^5\)$
Since $\(4=2^2\)$, this becomes:
$$
\(2^5 \times\left(2^2\right)^5=2^5 \times 2^{10}=2^{15}\)
$$
Equal to $\(8^5\)$.
- (B) $\(2^{15}\)$
Directly matches $\(8^5\)$.
- (C) $\(2 \times 4^7\)$
Since $\(4=2^2\)$, this becomes:
$$
\(2 \times\left(2^2\right)^7=2 \times 2^{14}=2^{15}\)
$$
Equal to $\(8^5\)$.
Conclusion:
All three expressions (A), (B), and (C) equal $\(8^5\)$.
gmatclubot
Re: Which of the following is equal to $8^5$ ? [#permalink]
16 Oct 2025, 12:43
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