Solve- 253-2-2433-5165-4- 84-3

(25)^3/2× (243)^3/5(16)^5/4× (8)^4/3 ⇒(5× 5)^3/2× (3× 3× 3× 3× 3)^3/5(2× 2× 2× 2)^5/4× (2× 2× 2)^4/3 ⇒(5^2)^3/2× (3^5)^3/5(2^4)^5/4× (2^3)^4/9 ...

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Byju's Answer

Standard VIII

Mathematics

Numbers in General Form

Solve: 253/...

Question

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

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Solution

$\frac{(25)^{3 / 2} \times (243)^{3 / 5}}{(16)^{5 / 4} \times (8)^{4 / 3}}$
$\Rightarrow \frac{(5 \times 5)^{3 / 2} \times (3 \times 3 \times 3 \times 3 \times 3)^{3 / 5}}{(2 \times 2 \times 2 \times 2)^{5 / 4} \times (2 \times 2 \times 2)^{4 / 3}}$
$\Rightarrow \frac{(5^{2})^{3 / 2} \times (3^{5})^{3 / 5}}{(2^{4})^{5 / 4} \times (2^{3})^{4 / 9}}$
$\Rightarrow \frac{5^{3} \times 3^{3}}{2^{5} \times 2^{4}}$
$\Rightarrow \frac{(5 \times 3)^{3}}{2^{9}}$ $∵ 9^{5} \times 9^{10} = 9^{15}$
$\Rightarrow \frac{15^{3}}{2^{9}}$ Answer

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Similar questions

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

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. Solve the following quadratic equations by factorization:

\frac{2 x}{x - 4} + \frac{2 x - 5}{x - 3} = \frac{25}{3}

Simplify :

$(i) 8^{\frac{4}{3}} + 25^{\frac{3}{2}} - {(\frac{1}{27})}^{- \frac{2}{3}} (i i) [(64)^{- 2}]^{- 3} \div [{(- 8)^{2}}^{3}]^{2} (i i i) (2^{- 3} - 2^{- 4}) (2^{- 3} + 2^{- 4})$

(81/16)–¾ * [(9/25)³/² ÷ (5/2)–³]

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Solve: (25)3/2×(243)3/5(16)5/4×84/3

(25)3/2×(243)3/5(16)5/4×(8)4/3⇒(5×5)3/2×(3×3×3×3×3)3/5(2×2×2×2)5/4×(2×2×2)4/3⇒(52)3/2×(35)3/5(24)5/4×(23)4/9⇒53×3325×24⇒(5×3)329 ∵95×910=915⇒15329 Answer

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