Question

Simplify this problems based on exponents. ​

Answer 1

Answer:

Question no (1)

${2}^ \frac{2}{3} \times {2}^ \frac{1}{3}$

$= = > 2 \: \frac{2}{3} + 2 \frac{1}{3 } \\ = = > 2 \frac{3}{3} = {2}^{1} = 2$

Question no 2

${7} \frac{5}{6} \times {7} \frac{2}{3}$

$= = > {7} \frac{5}{6} + \frac{2}{3} \\ = = > {7} \frac{5}{6} + \frac{2}{3} \\ = = > 7 \frac{5 + 4}{6 }$

$= = > 7\frac{9}{6} = 7 \ \frac{3}{2}$

Question no 3

$5 \ \frac{6}{7} - \frac{2}{3}$

$= = > 5 \ \frac{18 - 14}{21} \\ = = > 5 \ \frac{4}{21}$

Question no 4

$6 \ \frac{1}{2} \times 7 \ \frac{1}{2} \\ = = > 6 \times 7 \ \frac{1}{2} \\ = = > 42 \ \frac{1}{2}$

Question no 5

$( \frac{32}{243} )\ - \frac{4}{5} \\ = = > ( \frac{ {2}^{5} }{ {3}^{5} } ) \times ^{ \frac{ - 4}{5} }$

$= = > \frac{2}{3} \times ^{5} \times ^{ \frac{ - 4}{5} }$

$= = > \frac{2}{3} ^{ \frac{ - 4}{5} }$

$= = > \frac{3}{2} ^{ \frac{5}{4} }$

Question no 7

$(64) ^{ \frac{ - 1}{2 } } \\ = = > (2) ^{6 \times ^{ \frac{ - 1}{2} } }$

$= = > (2) ^{ - 3} = \frac{1}{ {2}^{3} } = \frac{1}{2 \times 2 \times 2} \\ = \frac{1}{8}$

Question No 8

${125}^{ \frac{1}{3} } \\ = = > {5}^{3 \times \frac{1}{3} } = 5 \\ = = > 5$

Question no 9

$(9) \: \frac{ 8^{ \frac{1}{2} } }{8 ^{ \frac{2}{3} } } \\ = = > 8 ^{ \frac{1}{2} - \frac{2}{3} } \\ = = > 8 ^{ \frac{3 - 4}{6} } \\ = = > 8 ^{ \frac{1}{6} }$

Question no 10

$(10) \: \: \: {3}^{ \frac{1}{4} } \times 5 ^{ \frac{1}{4} } \\ = = > 15 ^{ \frac{1}{4} }$

Hope it is helpful for you