Simplify? $\frac{2^{6}}{5^{6}} \times \frac{3^{6}}{4^{6}}$ $2^6/5^6xx3^6/4^6$

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Simplify? $\frac{2^{6}}{5^{6}} \times \frac{3^{6}}{4^{6}}$ $2^6/5^6xx3^6/4^6$

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Answer 1 · 2017-03-14T01:23:16

$\frac{729}{1, 000, 000} = 0.000729$ $729/(1,000,000)=0.000729$

Explanation:

We have

$\frac{2^{6}}{5^{6}} \times \frac{3^{6}}{4^{6}}$ $2^6/5^6xx3^6/4^6$

We can first combine the fractions:

$\frac{2^{6} \times 3^{6}}{5^{6} \times 4^{6}}$ $(2^6xx3^6)/(5^6xx4^6)$

We can rewrite $4^{6} = {(2^{2})}^{6} = 2^{2 \times 6} = 2^{12}$ $4^6=(2^2)^6=2^(2xx6)=2^12$

$\frac{2^{6} \times 3^{6}}{5^{6} \times 2^{12}}$ $(2^6xx3^6)/(5^6xx2^12)$

And so can cancel the terms with base 2:

$\frac{2^{0} \times 3^{6}}{5^{6} \times 2^{6}} = \frac{3^{6}}{5^{6} \times 2^{6}}$ $(2^0xx3^6)/(5^6xx2^6)=3^6/(5^6xx2^6)$

And from here we can evaluate the numbers:

$3^{6} = 729$ $3^6=729$
$5^{6} = 15625$ $5^6=15625$
$2^{6} = 64$ $2^6=64$

$\frac{3^{6}}{5^{6} \times 2^{6}} = \frac{729}{15625 \times 64} = \frac{729}{1, 000, 000} = 0.000729$ $3^6/(5^6xx2^6)=729/(15625xx64)=729/(1,000,000)=0.000729$

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Simplify? $\frac{2^{6}}{5^{6}} \times \frac{3^{6}}{4^{6}}$ $2^6/5^6xx3^6/4^6$

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Explanation:

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