(C) To solve $(729)^{\frac{1}{3}}$,we find the prime factorization of $729$.$729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^6$.Alternatively

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(C) To solve $(729)^{\frac{1}{3}}$,we find the prime factorization of $729$.$729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^6$.Alternatively,$729 = 9 \times 9 \times 9 = 9^3$.Therefore,$(729)^{\frac{1}{3}} = (9^3)^{\frac{1}{3}}$.Using the exponent rule $(a^m)^n = a^{m \times n}$,we get $9^{3 \times \frac{1}{3}} = 9^1 = 9$.

Class 9 Mathematics Number Systems Mix Examples - Number Systems

Easy

Fill in the blank to make the following statement true:
$(729)^{\frac{1}{3}} = \ldots$

A
$17$
B
$13$
C
$9$
D
$1$

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Class 9

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Number Systems

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Mix Examples - Number Systems

Prove that,$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}=1$.

Medium

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0 . \overline{001}$

Easy

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Find the value of $64^{-\frac{1}{3}}\left(64^{\frac{1}{3}}-64^{\frac{2}{3}}\right)$.

Easy

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Simplify: $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}$

Difficult

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Fill in the blank to make the following statement true:
$\sqrt[11]{1} = \ldots$

Easy

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Fill in the blank to make the following statement true:$(729)^{\frac{1}{3}} = \ldots$

Similar Questions

Prove that,$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}=1$.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0 . \overline{001}$

Find the value of $64^{-\frac{1}{3}}\left(64^{\frac{1}{3}}-64^{\frac{2}{3}}\right)$.

Simplify: $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}$

Fill in the blank to make the following statement true:$\sqrt[11]{1} = \ldots$

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Fill in the blank to make the following statement true:
$(729)^{\frac{1}{3}} = \ldots$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0 . \overline{001}$

Fill in the blank to make the following statement true:
$\sqrt[11]{1} = \ldots$