solve this Question brother and sister and reply me
Answers
Step-by-step explanation:
(
25
64
)
2
−3
= \frac{125}{512}
512
125
Explanation:
Given \left(\frac{64}{25}\right)^{\frac{-3}{2}}(
25
64
)
2
−3
= \left(\frac{25}{64}\right)^{\frac{3}{2}}(
64
25
)
2
3
/* By Exponential Law :*/
\boxed{\left(\frac{a}{b}\right)^{-n}=\left(\frac{b}{a}\right)^{n}}
(
b
a
)
−n
=(
a
b
)
n
= \left(\frac{5^{2}}{8^{2}}\right)^{\frac{3}{2}}(
8
2
5
2
)
2
3
= \left(\frac{5}{8}\right)^{2\times\frac{3}{2}}(
8
5
)
2×
2
3
/* By Exponential Law :*/
\boxed {\left(a^{m}\right)^{n}=a^{mn}}
(a
m
)
n
=a
mn
=\left(\frac{5}{8}\right)^{3}(
8
5
)
3
= \frac{5^{3}}{8^{3}}
8
3
5
3
/* By Exponential Law :*/
\boxed { \left(\frac{a}{b}\right)^{m} = \frac{a^{m}}{b^{m}}}
(
b
a
)
m
=
b
m
a
m
= \frac{5\times5\times5}{8\times8\times8}
8×8×8
5×5×5
= \frac{125}{512}
512
125
Therefore,
\left(\frac{64}{25}\right)^{\frac{-3}{2}}(
25
64
)
2
−3
= \frac{125}{512}
512
125