(64/125)-2⁄3+40×95/2×3-4-✓25/3✓64×(1/3)-1 simplify
Answers
Answer:
Answer:
(\frac{64}{125})^{\frac{-2}{3}}=\frac{25}{16}(
125
64
)
3
−2
=
16
25
Step-by-step explanation:
Given,(\frac{64}{125})^{\frac{-2}{3}}Given,(
125
64
)
3
−2
=(\frac{4^{3}}{5^{3}})^{\frac{-2}{3}}=(
5
3
4
3
)
3
−2
=(\big(\frac{4}{5}\big)^{3})^{\frac{-2}{3}}=((
5
4
)
3
)
3
−2
/* By Exponential Law:
\frac{a^{n}}{b^{n}}=(\frac{a}{b})^{n}
b
n
a
n
=(
b
a
)
n
=(\frac{4}{5})^{3\times \frac{-2}{3}}=(
5
4
)
3×
3
−2
=(\frac{4}{5})^{-2}=(
5
4
)
−2
\* By Exponential Law:
(a^{m})^{n}=a^{mn}(a
m
)
n
=a
mn
=(\frac{5}{4})^{2}=(
4
5
)
2
/* By Exponential Law:
(\frac{a}{b})^{-n}=(\frac{b}{a})^{n}(
b
a
)
−n
=(
a
b
)
n
\begin{gathered}=\frac{5^{2}}{4^{2}}\\=\frac{25}{16}\end{gathered}
=
4
2
5
2
=
16
25
Therefore,
(\frac{64}{125})^{\frac{-2}{3}}=\frac{25}{16}(
125
64
)
3
−2
=
16
25