Evaluatei 4216-23-1256-34-2243-15ii 64125-23-256625-14-370iii 8116-34259-32 - 52-3iv 2552 - 7291312523 - 2723 - 843

(i) 4216 23+1256 34+2243 15 4216 23+1256 34+2243 15=463 23+144 34+235 15=46 2+14 3+23 1=462+43+23=144+64+6=214 (ii) 64125 23+256625 14+370 64125 23+256625 14+ ...

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Byju's Answer

Standard VII

Mathematics

Addition of Integers

Evaluatei 421...

Question

Evaluate
(i) $\frac{4}{{(216)}^{- \frac{2}{3}}} + \frac{1}{{(256)}^{- \frac{3}{4}}} + \frac{2}{{(243)}^{- \frac{1}{5}}}$

(ii) ${(\frac{64}{125})}^{- \frac{2}{3}} + {(\frac{256}{625})}^{- \frac{1}{4}} + {(\frac{3}{7})}^{0}$

(iii) ${(\frac{81}{16})}^{- \frac{3}{4}} [{(\frac{25}{9})}^{- \frac{3}{2}} \div {(\frac{5}{2})}^{- 3}]$

(iv) $\frac{{(25)}^{\frac{5}{2}} \times {(729)}^{\frac{1}{3}}}{{(125)}^{\frac{2}{3}} \times {(27)}^{\frac{2}{3}} \times 8^{\frac{4}{3}}}$

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Solution

(i) $\frac{4}{{(216)}^{- \frac{2}{3}}} + \frac{1}{{(256)}^{- \frac{3}{4}}} + \frac{2}{{(243)}^{- \frac{1}{5}}}$
$\frac{4}{{(216)}^{- \frac{2}{3}}} + \frac{1}{{(256)}^{- \frac{3}{4}}} + \frac{2}{{(243)}^{- \frac{1}{5}}} = \frac{4}{{[{(6)}^{3}]}^{- \frac{2}{3}}} + \frac{1}{{[{(4)}^{4}]}^{- \frac{3}{4}}} + \frac{2}{{[{(3)}^{5}]}^{- \frac{1}{5}}} = \frac{4}{{(6)}^{- 2}} + \frac{1}{{(4)}^{- 3}} + \frac{2}{{(3)}^{- 1}} = 4 {(6)}^{2} + {(4)}^{3} + 2 (3) = 144 + 64 + 6 = 214$

(ii) ${(\frac{64}{125})}^{- \frac{2}{3}} + {(\frac{256}{625})}^{- \frac{1}{4}} + {(\frac{3}{7})}^{0}$
${(\frac{64}{125})}^{- \frac{2}{3}} + {(\frac{256}{625})}^{- \frac{1}{4}} + {(\frac{3}{7})}^{0} = {[{(\frac{4}{5})}^{3}]}^{- \frac{2}{3}} + {[{(\frac{4}{5})}^{4}]}^{- \frac{1}{4}} + 1 = {(\frac{4}{5})}^{- 2} + {(\frac{4}{5})}^{- 1} + 1 = {(\frac{5}{4})}^{2} + (\frac{5}{4}) + 1 = \frac{25}{16} + \frac{5}{4} + 1 = \frac{25 + 20 + 16}{16} = \frac{61}{16}$

(iii) ${(\frac{81}{16})}^{- \frac{3}{4}} [{(\frac{25}{9})}^{- \frac{3}{2}} \div {(\frac{5}{2})}^{- 3}]$
${(\frac{81}{16})}^{- \frac{3}{4}} [{(\frac{25}{9})}^{- \frac{3}{2}} \div {(\frac{5}{2})}^{- 3}] = {(\frac{16}{81})}^{\frac{3}{4}} [{(\frac{9}{25})}^{\frac{3}{2}} \div {(\frac{2}{5})}^{3}] = {[{(\frac{2}{3})}^{4}]}^{\frac{3}{4}} \{{[{(\frac{3}{5})}^{2}]}^{\frac{3}{2}} \div (\frac{8}{125})\} = {(\frac{2}{3})}^{3} [{(\frac{3}{5})}^{3} \div (\frac{8}{125})] = \frac{\frac{8}{27} \times \frac{27}{125}}{\frac{8}{125}} = 1$

(iv) $\frac{{(25)}^{\frac{5}{2}} \times {(729)}^{\frac{1}{3}}}{{(125)}^{\frac{2}{3}} \times {(27)}^{\frac{2}{3}} \times 8^{\frac{4}{3}}}$
$\frac{{(25)}^{\frac{5}{2}} \times {(729)}^{\frac{1}{3}}}{{(125)}^{\frac{2}{3}} \times {(27)}^{\frac{2}{3}} \times 8^{\frac{4}{3}}} = \frac{{[{(5)}^{2}]}^{\frac{5}{2}} \times {[{(9)}^{3}]}^{\frac{1}{3}}}{{[{(5)}^{3}]}^{\frac{2}{3}} \times {[{(3)}^{3}]}^{\frac{2}{3}} \times {[{(2)}^{3}]}^{\frac{4}{3}}} = \frac{{(5)}^{5} \times {(9)}^{1}}{{(5)}^{2} \times {(3)}^{2} \times {(2)}^{4}} = \frac{5 \times 5 \times 5 \times 5 \times 5 \times 9}{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2} = \frac{125}{16}$

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Similar questions

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(i)

(3^{2} + 2^{2}) \times {(\frac{1}{2})}^{3}

(ii)

(3^{2} - 2^{2}) \times {(\frac{2}{3})}^{- 3}

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Q. Prove that
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Evaluate (i) 4216-23+1256-34+2243-15 (ii) 64125-23+256625-14+370 (iii) 8116-34 259-32÷52-3 (iv) 2552×7291312523×2723×843