5 raised to 7 × 5 raised to 6
Answers
Answer :-
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Answer:
The value of x is 5
Given,
\begin{gathered}(\frac{5}{7} )^{6} (\frac{7}{5} )^{-9} = (\frac{5}{7})^{3x} \\\\\end{gathered}
(
7
5
)
6
(
5
7
)
−9
=(
7
5
)
3x
----------------(1)
We know that,
a^{-m} = \frac{1}{a^{m} }a
−m
=
a
m
1
(\frac{7}{5})^{-9} = \frac{1}{(\frac{7}{5})^{9} } = (\frac{5}{7} )^{9}(
5
7
)
−9
=
(
5
7
)
9
1
=(
7
5
)
9
Substituting above value in (1), it becomes
(\frac{5}{7})^{6} (\frac{5}{7})^{9} = (\frac{5}{7})^{3x}(
7
5
)
6
(
7
5
)
9
=(
7
5
)
3x
-------------------(2)
Bases are same, powers must be added
a^{m} a^{n} = a^{m+n}a
m
a
n
=a
m+n
Applying above rule in (2), we get
\begin{gathered}(\frac{5}{7} )^{6+9} = (\frac{5}{7} )^{3x} \\(\frac{5}{7} )^{15} = (\frac{5}{7} )^{3x}\end{gathered}
(
7
5
)
6+9
=(
7
5
)
3x
(
7
5
)
15
=(
7
5
)
3x
Bases are same in equation, powers must be equated
a^{m} = a^{n}a
m
=a
n
⇒ m = nm=n
Using above rule, we get
15 = 3x
x = \frac{15}{3}
3
15
=