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Algebra Difficulty 1.3 Junior Find the answer Canada

If $2^n = 8^{20}$ , what is the value of $n$ ?

$10$
$60$
$40$
$16$
$17$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solutions — 2

Solution 1

Since $8 = 2 \times 2 \times 2 = 2^3$ , then $8^{20} = (2^3)^{20} = 2^{3 \times 20} = 2^{60}$ .

Thus, if $2^n = 8^{20}$ , then $n = 60$ .

Solution 2

Since $8 = 2 \times 2 \times 2 = 2^3$ , then $8^{20} = (2^3)^{20} = 2^{3 \times 20} = 2^{60}$ .
Thus, if $2^n = 8^{20}$ , then $n = 60$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.