How do you evaluate $\frac{6^{5}}{6^{2}}$ $6^5/6^2$ ?

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How do you evaluate $\frac{6^{5}}{6^{2}}$ $6^5/6^2$ ?

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Answer 1 · 2018-04-02T13:25:18

$6^{3}$ $6^3$ = 216

Explanation:

Using the index laws
$\frac{a^{m}}{a^{n}}$ $(a^m)/(a^n)$ = $a^{m - n}$ $a^(m-n)$

$\frac{6^{5}}{6^{2}}$ $6^5/6^2$ = $6^{5 - 2}$ $6^(5-2)$ = $6^{3}$ $6^3$ = 216

Answer 2 · 2018-04-02T13:27:23

$6^{3}$ $6^3$ = 216

Explanation:

When dividing two numbers with exponents, which have the same base, you can just subtract the exponents from eachother like this:
$\frac{a^{b}}{a^{c}} = a^{b - c}$ $(a^b)/(a^c) = a^(b-c)$
and similarly (eventhough its not relevant to this problem,)
$(a^{b}) \cdot (a^{c}) = a^{b + c}$ $(a^b)*(a^c) = a^(b+c)$
therefor:
$\frac{6^{5}}{6^{2}} = 6^{5 - 2} = 6^{3} = 6 \cdot 6 \cdot 6 = 216$ $(6^5)/(6^2) = 6^(5-2) = 6^3 = 6*6*6 = 216$

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How do you evaluate $\frac{6^{5}}{6^{2}}$ $6^5/6^2$ ?

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