Express the following rational numbers in power notation:
$- \frac{64}{125}$

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Solution

Given $- \frac{64}{125} = - \frac{4 \times 4 \times 4}{5 \times 5 \times 5}$
$= - \frac{4^{3}}{5^{3}} = - {(\frac{4}{5})}^{3} = {(- \frac{4}{5})}^{3}$

Hence, $- \frac{64}{125} = {(- \frac{4}{5})}^{3}$

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Similar questions

Q. Express each of the following rational numbers in power notation:
(i)

\frac{49}{64}

(ii)

- \frac{64}{125}

(iii)

- \frac{1}{216}

Q. Express each of the following rational numbers in standard form:
(i)

\frac{- 12}{30}

(ii)

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(iii)

\frac{24}{- 64}

(iv)

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Express each of the following rational numbers as the sum of an integer and a rational number:
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(ii) $\frac{- 11}{7}$
(iii) $\frac{- 25}{9}$
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Q. Express the following rational numbers in exponential notations. Further express them as power of prime factors. -1/125.

Question 94

Solve the following:

Express $\frac{27}{64}$ and $\frac{- 27}{64}$ as powers of a rational number.

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Express the following rational numbers in power notation:−64125

Given −64125=−4×4×45×5×5=−4353=−(45)3=(−45)3Hence, −64125=(−45)3

Express the following rational numbers in power notation:
$- \frac{64}{125}$

Given $- \frac{64}{125} = - \frac{4 \times 4 \times 4}{5 \times 5 \times 5}$
$= - \frac{4^{3}}{5^{3}} = - {(\frac{4}{5})}^{3} = {(- \frac{4}{5})}^{3}$

Hence, $- \frac{64}{125} = {(- \frac{4}{5})}^{3}$