Question

Indices Chapter
a. (64)³/⁶
b.(625/1296)¾
c.
$\sqrt[5]{ \frac{243}{1024} }$
d.
$( \frac{1}{128} )^{ \frac{1}{7} } + ( \frac{1}{64})^{ \frac{1}{6} }$

e.
$( \frac{81}{16} )^{ \frac{ - 3}{4} }$
Find The Answer By The Indices Rule​

Answer 1

Answer:

1. ${64}^{ \frac{3}{6} }$

${64}^{ \frac{1}{2} }$

√64

=8

$2.({ \frac{625}{1296} })^{ \frac{3}{4} }$

$= {( \frac{ {5}^{4} }{ {6}^{4} }) }^{ \frac{3}{4} }$

$= \frac{ {5}^{3} }{ {6}^{3} }$

$= \frac{125}{216}$

$3.\sqrt[5]{ \frac{243}{1024} }$

$= \sqrt[5]{ \frac{ {3}^{5} }{ {4}^{5} } }$

$= ( { \frac{ {3}^{5} }{ {4}^{5} } })^{ \frac{1}{5} }$

$= \frac{ {3}^{1} }{ {4}^{1} }$

=$\frac{3}{4}$

$4. \: ({ \frac{1}{128} })^{7} + \: ({ \frac{1}{64} })^{6}$

$= ({ \frac{ {1}^{7} }{ {2}^{7} } })^{ \frac{1}{7} } + ({ \frac{ {1}^{6} }{ {2}^{6} } })^{ \frac{1}{6} }$

$= \frac{1}{2} + \frac{1}{2}$

$= 1$

$5. { \:({ \frac{81}{16} })}^{ \frac{ - 3}{4} }$

$= \: ({ \frac{ {3}^{4} }{ {2}^{4} } \: })^{ \frac{ - 3}{4} }$

$= \: ({ \frac{ {2}^{4} }{ {3}^{4} } \: })^{ \frac{ 3}{4} }$

$= \frac{ {2}^{3} }{ {3}^{3} }$

$= \frac{8}{27}$

Hope it helps...

Mark as brainliest......

In the 4th question sorry I wrote power 7 it's 1/7 the answer is right check.