(B) Given expression: $(\frac{1}{27})^{\frac{-2}{3}}$First,express $27$ as a power of $3$: $27 = 3^3$.So,$\frac{1}{27} = \frac{1}{3^3} = 3^{-3}$.Now,s

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(B) Given expression: $(\frac{1}{27})^{\frac{-2}{3}}$First,express $27$ as a power of $3$: $27 = 3^3$.So,$\frac{1}{27} = \frac{1}{3^3} = 3^{-3}$.Now,substitute this into the expression:$(3^{-3})^{\frac{-2}{3}}$Using the power rule $(a^m)^n = a^{m \times n}$:$3^{-3 \times \frac{-2}{3}} = 3^2$Finally,calculate the value:$3^2 = 9$.

Class 9 Mathematics Number Systems Mix Examples - Number Systems

Medium

Simplify: $(\frac{1}{27})^{\frac{-2}{3}}$

A
$3$
B
$9$
C
$81$
D
$27$

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Mix Examples - Number Systems

Express $1.23\overline{4}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Medium

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Visualise $2.365$ on the number line,using successive magnification.

Medium

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Rationalise the denominator of the following:
$\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}}$

Difficult

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Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{29}{12}$

Medium

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Simplify: $64^{-\frac{1}{3}} + 64^{\frac{1}{3}} - 64^{\frac{2}{3}}$

Medium

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Simplify: $(\frac{1}{27})^{\frac{-2}{3}}$

Similar Questions

Express $1.23\overline{4}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Visualise $2.365$ on the number line,using successive magnification.

Rationalise the denominator of the following:$\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}}$

Convert the following rational number into decimal form and state the kind of its decimal expansion:$\frac{29}{12}$

Simplify: $64^{-\frac{1}{3}} + 64^{\frac{1}{3}} - 64^{\frac{2}{3}}$

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Rationalise the denominator of the following:
$\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}}$

Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{29}{12}$