State True or False.
Simplifying and expressing as positive indices ${(\frac{125 a^{- 3}}{y^{6}})}^{- \frac{1}{3}}$ , we get $\frac{a y^{2}}{5}$ .

True

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False

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Solution

The correct option is A True
As given ${(\frac{125 a^{- 3}}{y^{6}})}^{- \frac{1}{3}}$

$\Rightarrow {(\frac{5^{3} a^{- 3}}{y^{6}})}^{- \frac{1}{3}}$
$\Rightarrow ⎛ ⎜ ⎝ \frac{5^{3 \cdot - \frac{1}{3}} a^{- 3 \cdot - \frac{1}{3}}}{y^{6 \cdot - \frac{1}{3}}} ⎞ ⎟ ⎠$
$\Rightarrow (\frac{5^{- 1} a^{1}}{y^{- 2}})$
$\Rightarrow \frac{a y^{2}}{5}$

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