(D) To find the value of $64^{\frac{2}{3}}$,we first express $64$ as a power of $2$ or $4$.Since $64 = 4^3$,we can write the expression as:$64^{\frac{

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(D) To find the value of $64^{\frac{2}{3}}$,we first express $64$ as a power of $2$ or $4$.Since $64 = 4^3$,we can write the expression as:$64^{\frac{2}{3}} = (4^3)^{\frac{2}{3}}$.Using the exponent rule $(a^m)^n = a^{m \times n}$,we get:$4^{3 \times \frac{2}{3}} = 4^2$.Calculating the value,$4^2 = 16$.

Class 9 Mathematics Number Systems Mix Examples - Number Systems

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Find the value of $64^{\frac{2}{3}}$.

A
$15$
B
$24$
C
$22$
D
$16$

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Mix Examples - Number Systems

Find the value of $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$.

Medium

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Express $2.\overline{137}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

Medium

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Rationalise the denominator of the following:
$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Difficult

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Rationalise the denominator in each of the following:
$\frac{1}{7-4 \sqrt{3}}$

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Represent $\sqrt{7.5}$ on the number line.

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Find the value of $64^{\frac{2}{3}}$.

Similar Questions

Find the value of $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$.

Express $2.\overline{137}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

Rationalise the denominator of the following:$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Rationalise the denominator in each of the following:$\frac{1}{7-4 \sqrt{3}}$

Represent $\sqrt{7.5}$ on the number line.

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Rationalise the denominator of the following:
$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

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$\frac{1}{7-4 \sqrt{3}}$