Prove that - 3-3- 62-9852-1-25- 15-4-3- 31-3 - 28-2

Given, 3^ 3× 6^2 ×√(98)5^2 ×√(1/25)× 15^ 4/3× 3^1/3 =6^2× 98^1/25^2× 15^ 4/3× 3^10/3(1/25)^1/3 =2^2× 3^2× 98^1/25^2× 3^ 4/3× 5^ 4/3× 3^10/3(1/25)^ ...

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Byju's Answer

Standard XII

Mathematics

nCr Definitions and Properties

Prove that : ...

Question

Prove that :
$\frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{1 / 25} \times (15)^{- 4 / 3} \times 3^{1 / 3}} = 28 \sqrt{2}$

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Solution

Given,

$\frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{\frac{1}{25}} \times 15^{- \frac{4}{3}} \times 3^{\frac{1}{3}}}$

$= \frac{6^{2} \times 98^{\frac{1}{2}}}{5^{2} \times 15^{- \frac{4}{3}} \times 3^{\frac{10}{3}} {(\frac{1}{25})}^{\frac{1}{3}}}$

$= \frac{2^{2} \times 3^{2} \times 98^{\frac{1}{2}}}{5^{2} \times 3^{- \frac{4}{3}} \times 5^{- \frac{4}{3}} \times 3^{\frac{10}{3}} {(\frac{1}{25})}^{\frac{1}{3}}}$

$= \frac{2^{2} \times 3^{2} \times 98^{\frac{1}{2}}}{5^{2} \times 5^{- \frac{4}{3}} \times 3^{\frac{10}{3} - \frac{4}{3}} {(\frac{1}{25})}^{\frac{1}{3}}}$

$= \frac{2^{2} \times 98^{\frac{1}{2}}}{5^{2} \times 5^{- \frac{4}{3}} {(\frac{1}{25})}^{\frac{1}{3}}}$

$= \frac{2^{2} \times 7 \times 2^{\frac{1}{2}}}{5^{2} \times \frac{1}{5 \times 5^{\frac{1}{3}}} \times \frac{1}{25^{\frac{1}{3}}}}$

$= \frac{2^{2} \times 7 \times 2^{\frac{1}{2}}}{1}$

$= 28 \sqrt{2}$ $[h e n c e p r o v e d]$

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Similar questions

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

Q. 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}

(ii)

9^{3 / 2} - 3 \times 5^{0} - {(\frac{1}{81})}^{-}^{1 / 2} = 15

(iii)

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

(iv)

\frac{2^{1 / 2} \times 3^{1 / 3} \times 4^{1 / 4}}{10^{- 1 / 5} \times 5^{3 / 5}} \div \frac{3^{4 / 3} \times 5^{- 7 / 5}}{4^{- 3 / 5} \times 6} = 10

(v)

\sqrt{\frac{1}{4} + (0.01)^{- 1 / 2}} - (27)^{2 / 3} = \frac{3}{2}

(vi)

\frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}} = \frac{3}{2}

(vii)

{(\frac{64}{125})}^{- 2 / 3} + \frac{1}{{(\frac{256}{625})}^{1 / 4}} + (\frac{\sqrt{25}}{\sqrt[3]{64}}) = \frac{65}{16}

(viii)

\frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{1 / 25} \times (15) -^{4 / 3} \times 3^{1 / 3}} = 28 \sqrt{2}

(ix)

\frac{(0.6)^{0} - (0.1) - 1}{{(\frac{3}{8})}^{- 1} {(\frac{3}{2})}^{3} + {(- \frac{1}{3})}^{- 1}} = - \frac{3}{2}

Q. Find the values of the following using formulae.

(1) 52²
(2) 98²
(3) 63²
(4) 32 × 28
(5) 77 × 83

Find x, if

$(i) {(\frac{1}{4})}^{- 4} \times {(\frac{1}{4})}^{- 8} = {(\frac{1}{4})}^{- 4 x} (i i) {(\frac{- 1}{2})}^{- 19} \div {(\frac{- 1}{2})}^{8} = {(\frac{- 1}{2})}^{- 2 x + 1} (i i i) {(\frac{3}{2})}^{- 3} \div {(\frac{3}{2})}^{5} = {(\frac{3}{2})}^{2 x + 1} (i v) {(\frac{2}{5})}^{- 3} \times {(\frac{2}{5})}^{15} = {(\frac{2}{5})}^{2 + 3 x} (v) {(\frac{5}{4})}^{- x} \div {(\frac{5}{4})}^{- 4} = {(\frac{5}{4})}^{5} (v i) {(\frac{8}{3})}^{2 x + 1} \times {(\frac{8}{3})}^{5} = {(\frac{8}{3})}^{x + 2}$

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Prove that : 3−3×62×√9852×3√1/25×(15)−4/3×31/3=28√2

Given,3−3×62×√9852×3√125×15−43×313=62×981252×15−43×3103(125)13=22×32×981252×3−43×5−43×3103(125)13=22×32×981252×5−43×3103−43(125)13=22×981252×5−43(125)13=22×7×21252×15×513×12513=22×7×2121=28√2 [henceproved]

Prove that :
$\frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{1 / 25} \times (15)^{- 4 / 3} \times 3^{1 / 3}} = 28 \sqrt{2}$