$(243)^{\frac{3}{5}}$ = ___

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Solution

$(243)^{\frac{3}{5}}$ = $(3^{5})^{\frac{3}{5}}$

$∵ ((a)^{m})^{n} = (a)^{(m \times n)}$

$\Rightarrow 3^{3}$ = 27

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Similar questions

Q. Solve:

\frac{(25)^{3 / 2} \times (243)^{3 / 5}}{(16)^{5 / 4} \times 8^{4 / 3}}

$\frac{{(243)}^{\frac{n}{5}} \times 3^{2 n + 1}}{9^{n} \times 3^{n - 1}} = ?$

Q. Simplify:

(i)

(16^{- 1 / 5})^{5 / 2}

(ii)

\sqrt[5]{{(32)}^{- 3}}

(iii)

\sqrt[3]{(343)^{- 2}}

(iv)

(0.001)^{1 / 3}

(v)

\frac{(25)^{3 / 2} \times (243)^{3 / 5}}{(16)^{5 / 4} \times (8)^{4 / 3}}

(vi)

{(\frac{\sqrt{2}}{5})}^{8} \div {(\frac{\sqrt{2}}{5})}^{13}

(vii)

{(\frac{5^{- 1} \times 7^{2}}{5^{2} \times 7^{- 4}})}^{7 / 2} \times {(\frac{5^{- 2} \times 7^{3}}{5^{3} \times 7^{- 5}})}^{- 5 / 2}

Q. Explain with reason whether the given number is perfect square or not:

2433

Simplify:

(i) $(16^{\frac{- 1}{5}})^{\frac{5}{2}}$

(ii) $\sqrt[5]{(32)^{- 3}}$

(iii) $\sqrt[3]{(343)^{- 2}}$

(iv) $(0.001)^{\frac{1}{3}}$

(v) $\frac{(25)^{\frac{3}{2}} \times (243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} \times (8)^{\frac{4}{3}}}$

(vi) ${(\frac{\sqrt{2}}{5})}^{8} \div {(\frac{\sqrt{2}}{5})}^{13}$

(vii) ${(\frac{5^{- 1} \times 7^{2}}{5^{2} \times 7^{- 4}})}^{\frac{7}{2}} \times {(\frac{5^{- 2} \times 7^{3}}{5^{3} \times 7^{- 5}})}^{\frac{- 5}{2}}$

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(243)35 = ___

(243)35 = (35)35 ∵((a)m)n=(a)(m×n) ⇒ 33 = 27

$(243)^{\frac{3}{5}}$ = ___

$(243)^{\frac{3}{5}}$ = $(3^{5})^{\frac{3}{5}}$

$∵ ((a)^{m})^{n} = (a)^{(m \times n)}$

$\Rightarrow 3^{3}$ = 27