Express each of the following rational numbers in power notation.
a. $\frac{-125}{216}$
b. $\frac{64}{729}$

Given :

The given numbers are,

b. $\frac{64}{729}$.

To do :

We have to express the given rational numbers in power notation.

Solution :

We know that,

$(\frac{a}{b})^3 = \frac{a^3}{b^3}$

a. $\frac{-125}{216}$

$-125 = -(5\times 5\times 5) = -(5)^3$.

$216 = 6\times 6\times 6 = 6^3$.

Therefore,

$\frac{-125}{216} = \frac{(-5)^3}{(6)^3}= (\frac{-5}{6})^3$.

Therefore, $\frac{-125}{216}$ in power notation is  $(\frac{-5}{6})^3$.

b. $\frac{64}{729}$.

$64 = 4\times 4 \times 4 =4^3$

$729=9\times 9\times 9 = 9^3$

Therefore,

$\frac{64}{729}= \frac{4^3}{9^3}=(\frac{4}{9})^3$.

Therefore, $\frac{64}{729}$ in power notation is $(\frac{4}{9})^3$.

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Updated on: 10-Oct-2022

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