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Express in exponent form.
a)$\frac{64}{125} $
b)$\quad \frac{-8}{342}$c)$625$
d) $\frac{16}{81}$
Solution:
a) $\frac{64}{125} $
$64 = 4 \times 4 \times 4 = 4^3$
$125 = 5 \times 5 \times 5 = 5^3$
$\frac{64}{125} $ = $\left(\frac{4^{3}}{5^{3}}\right)$
The powers are same, so
$\frac{64}{125} $ = $ \left(\frac{4}{5}\right)^{3} $
b) $\quad \frac{-8}{342}$
$-8 = -2 \times -2 \times -2 = (-2)^3$
$343 = 7 \times 7 \times 7 = 7^3$
$\quad \frac{-8}{342}$ = $\left(\frac{-2^{3}}{7^{3}}\right)$
$\quad \frac{-8}{342}$ = $ \left(\frac{-2}{7}\right)^{3} $
c)$625$
= $5 \times 5 \times 5 \times 5$
= $5^4$
$625 = 5^4$
d)$\frac{16}{81}$
$16 = 2 \times 2 \times 2 \times 2 = 2^4$
$81 = 3 \times 3 \times 3 \times 3 = 3^4$
$\frac{16}{81}$ = $\left(\frac{2^{4}}{3^{4}}\right)$
$\frac{16}{81}$ = $ \left(\frac{2}{3}\right)^{4} $