Simplifyi 1513914-6ii 1215271552iii 1514312-2

(i) 1513914 6 1513914 6=91415136 #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; ...

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Byju's Answer

Standard VI

Mathematics

Subtraction of Integers

Simplifyi 151...

Question

Simplify
(i) ${(\frac{15^{\frac{1}{3}}}{9^{\frac{1}{4}}})}^{- 6}$

(ii) ${(\frac{12^{\frac{1}{5}}}{27^{\frac{1}{5}}})}^{\frac{5}{2}}$

(iii) ${(\frac{15^{\frac{1}{4}}}{3^{\frac{1}{2}}})}^{- 2}$

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Solution

(i) ${(\frac{15^{\frac{1}{3}}}{9^{\frac{1}{4}}})}^{- 6}$
${(\frac{15^{\frac{1}{3}}}{9^{\frac{1}{4}}})}^{- 6} = {(\frac{9^{\frac{1}{4}}}{15^{\frac{1}{3}}})}^{6} = \frac{9^{\frac{6}{4}}}{15^{\frac{6}{3}}} = \frac{9^{\frac{3}{2}}}{15^{2}} = \frac{{(3^{2})}^{\frac{3}{2}}}{15^{2}} = \frac{3^{3}}{15^{2}} = \frac{27}{225} = \frac{3}{25}$

(ii) ${(\frac{12^{\frac{1}{5}}}{27^{\frac{1}{5}}})}^{\frac{5}{2}}$
${(\frac{12^{\frac{1}{5}}}{27^{\frac{1}{5}}})}^{\frac{5}{2}} = \frac{{(12^{\frac{1}{5}})}^{\frac{5}{2}}}{{(27^{\frac{1}{5}})}^{\frac{5}{2}}} = \frac{12^{\frac{1}{2}}}{27^{\frac{1}{2}}} = {(\frac{12}{27})}^{\frac{1}{2}} = {(\frac{4}{9})}^{\frac{1}{2}} = {[{(\frac{2}{3})}^{2}]}^{\frac{1}{2}} = \frac{2}{3}$

(iii) ${(\frac{15^{\frac{1}{4}}}{3^{\frac{1}{2}}})}^{- 2}$
${(\frac{15^{\frac{1}{4}}}{3^{\frac{1}{2}}})}^{- 2} = {(\frac{3^{\frac{1}{2}}}{15^{\frac{1}{4}}})}^{2} = \frac{3^{\frac{2}{2}}}{15^{\frac{2}{4}}} = \frac{3}{15^{\frac{1}{2}}} = \frac{3}{3^{\frac{1}{2}} . 5^{\frac{1}{2}}} = \frac{3^{1 - \frac{1}{2}}}{5^{\frac{1}{2}}} = \frac{3^{\frac{1}{2}}}{5^{\frac{1}{2}}} = \sqrt{\frac{3}{5}}$

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Similar questions

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Simplifyi:(7+3√5\3+√5)+(7-3√5\3-√5

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Simplify (i) 1513914-6 (ii) 1215271552 (iii) 1514312-2

(i) 1513914-6 1513914-6=91415136 =9641563 =932152 =3232152 =33152 =27225 =325 (ii) 1215271552 1215271552=121552271552 =12122712 =122712 =4912 =23212 =23 (iii) 1514312-2 1514312-2=31215142 =3221524 =31512 =3312.512 =31-12512 =312512 =35

Simplify
(i) ${(\frac{15^{\frac{1}{3}}}{9^{\frac{1}{4}}})}^{- 6}$

(ii) ${(\frac{12^{\frac{1}{5}}}{27^{\frac{1}{5}}})}^{\frac{5}{2}}$

(iii) ${(\frac{15^{\frac{1}{4}}}{3^{\frac{1}{2}}})}^{- 2}$