Prove that 8116-3 - 4 - 259-3 - 2 - 52-3-1-

8116 34 #215;259 32 #247;52 3=168134 #215;92532 #215;52–3=234 #215;34 #215;352 #215;32 #215;523=233 #215;353 #215;523=23 #215;33 #215;53 ...

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Byju's Answer

Standard IX

Mathematics

Properties of Multiplication of Integers

Prove that 81...

Question

Prove that ${(\frac{81}{16})}^{- 3 / 4} \times \{{(\frac{25}{9})}^{- 3 / 2} \div {(\frac{5}{2})}^{- 3}\} = 1$ .

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Solution

${(\frac{81}{16})}^{\frac{- 3}{4}} \times \{{(\frac{25}{9})}^{\frac{- 3}{2}} \div {(\frac{5}{2})}^{- 3}\} = {(\frac{16}{81})}^{\frac{3}{4}} \times \{{(\frac{9}{25})}^{\frac{3}{2}} \times {(\frac{5}{2})}^{- (- 3)}\} = {(\frac{2}{3})}^{4 \times \frac{3}{4}} \times {(\frac{3}{5})}^{2 \times \frac{3}{2}} \times {(\frac{5}{2})}^{3} = {(\frac{2}{3})}^{3} \times {(\frac{3}{5})}^{3} \times {(\frac{5}{2})}^{3} = \frac{2^{3} \times 3^{3} \times 5^{3}}{3^{3} \times 5^{3} \times 2^{3}} = 1$

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Similar questions

Q. If

{(\frac{2}{3})}^{x} {(\frac{3}{2})}^{2 x} = \frac{81}{16} then x = ?

(a) 1
(b) 2
(c) 3
(d) 4

Q. Prove that

∣ ∣ ∣ ∣ \begin{matrix} 1! & 2! & 3! 2! & 3! & 4! 3! & 4! & 5! \end{matrix} ∣ ∣ ∣ ∣ = 4!

{(\frac{81}{16})}^{- 3 / 4} = ?

(a)

\frac{4}{9}

(b)

\frac{9}{4}

(c)

\frac{27}{8}

(d)

\frac{8}{27}

Prove that :

$(i) (\sqrt{3 \times 5^{- 3}} \div \sqrt[3]{3^{- 1}} \sqrt{5}) \times \sqrt[6]{3 \times 5^{6}} = \frac{3}{5} (i i) 9^{\frac{3}{2}} - 3 \times 5^{0} - {(\frac{1}{81})}^{\frac{- 1}{2}} = 15 (i i i) {(\frac{1}{4})}^{- 2} - 3 \times 8^{\frac{2}{3}} \times 4^{0} + {(\frac{9}{16})}^{\frac{- 1}{2}} = \frac{16}{3} (i v) \frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 4^{\frac{1}{4}}}{10^{\frac{- 1}{5}} \times 5^{\frac{3}{5}}} \div \frac{3^{\frac{4}{3}} \times 5^{\frac{- 7}{5}}}{4^{\frac{- 3}{5}} \times 6} = 10 (v) \sqrt{\frac{1}{4}} + (0.01)^{\frac{- 1}{2}} - (27)^{\frac{2}{3}} = \frac{3}{2} (v i) \frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}} = \frac{3}{2} (v i i) {(\frac{64}{125})}^{\frac{- 2}{3}} + \frac{1}{{(\frac{256}{625})}^{\frac{1}{4}}} + {(\frac{\sqrt{25}}{\sqrt[3]{64}})}^{0} = \frac{61}{16} (v i i i) \frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{\frac{1}{25}} \times (15)^{\frac{- 4}{3}} \times 3^{\frac{1}{3}}} = 28 \sqrt{2} (i x) \frac{(0.6)^{0} - (0.1)^{- 1}}{{(\frac{3}{8})}^{- 1} {(\frac{3}{2})}^{3} + {(\frac{1}{3})}^{- 1}} = - \frac{3}{2}$

Q. Prove that:

{(\frac{1}{4})}^{- 2} - 3 \times 8^{\frac{2}{3}} \times 4^{0} + {(\frac{9}{16})}^{- \frac{1}{2}} = \frac{16}{3}

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Prove that 8116-3/4×259-3/2÷52-3=1.

8116-34×259-32÷52-3=168134×92532×52--3=234×34×352×32×523=233×353×523=23×33×5333×53×23=1

Prove that ${(\frac{81}{16})}^{- 3 / 4} \times \{{(\frac{25}{9})}^{- 3 / 2} \div {(\frac{5}{2})}^{- 3}\} = 1$ .