find the equation
Answers
Answer:
Given Question
\pink{ \tt \: :\implies \: {(125)}^{ - \frac{2}{3} } \times {(625)}^{ \frac{5}{4} } \div {( \frac{1}{5} )}^{ - 3} }:⟹(125)
−
3
2
×(625)
4
5
÷(
5
1
)
−3
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\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}
FormulaUsed:
\begin{gathered}\begin{gathered}(1)\:{\underline{\boxed{\bf{\blue{a^m\times{a^n}\:=\:a^{m\:+\:n}\:}}}}} \\ \end{gathered}\end{gathered}
(1)
a
m
×a
n
=a
m+n
\begin{gathered}\begin{gathered}(2)\:{\underline{\boxed{\bf{\purple{\dfrac{a^m}{a^n}\:=\:a^{m\:-\:n}\:}}}}} \\ \end{gathered}\end{gathered}
(2)
a
n
a
m
=a
m−n
\begin{gathered}\begin{gathered}(3)\:{\underline{\boxed{\bf{\orange{\dfrac{1}{x^n}\:=\:x^{-n}\:}}}}} \\ \end{gathered}\end{gathered}
(3)
x
n
1
=x
−n
\begin{gathered}\begin{gathered}(4)\:{\underline{\boxed{\bf{\color{peru}{(a^m)^n\:=\:a^{m\times{n}}\:}}}}} \\ \end{gathered}\end{gathered}
(4)
(a
m
)
n
=a
m×n
\begin{gathered}\begin{gathered}(5)\:{\underline{\boxed{\bf{\red{ {x}^{0} = 1}}}}} \\ \end{gathered}\end{gathered}
(5)
x
0
=1
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\large\underline\purple{\bold{Solution :- }}
Solution:−
\tt \: :\implies \: {(125)}^{ - \frac{2}{3} } \times {(625)}^{ \frac{5}{4} } \div {( \frac{1}{5} )}^{ - 3} :⟹(125)
−
3
2
×(625)
4
5
÷(
5
1
)
−3
\tt \: :\implies \: {(5 \times 5 \times 5)}^{ - \frac{2}{3} } \times {(5 \times 5 \times 5 \times 5)}^{ \frac{5}{4} } \times {(5)}^{ - 3} :⟹(5×5×5)
−
3
2
×(5×5×5×5)
4
5
×(5)
−3
\tt \: :\implies \: {(5)}^{ - \frac{2}{3} \times 3 } \times {(5)}^{ \frac{5}{4} \times 4} \times {(5)}^{ - 3} :⟹(5)
−
3
2
×3
×(5)
4
5
×4
×(5)
−3
\tt \: :\implies \: {(5)}^{ - 2} \times {(5)}^{5} \times {(5)}^{ - 3} :⟹(5)
−2
×(5)
5
×(5)
−3
\tt \: :\implies \: {(5)}^{ - 2 + 5 - 3} :⟹(5)
−2+5−3
\tt \: :\implies \: {(5)}^{0} :⟹(5)
0
\tt \: :\implies \: 1:⟹1
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Step-by-step explanation:
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