find the value of x for which (5/3)^-4*(3/5)^-5=(3/5)^3x
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ANSWER
The value of x is -3.
Step-by-step explanation:
Given : Expression (\frac{5}{3})^{-4}\times (\frac{5}{3})^{-5}=(\frac{5}{3})^{3x}(
3
5
)
−4
×(
3
5
)
−5
=(
3
5
)
3x
To find : The value of x ?
Solution :
(\frac{5}{3})^{-4}\times (\frac{5}{3})^{-5}=(\frac{5}{3})^{3x}(
3
5
)
−4
×(
3
5
)
−5
=(
3
5
)
3x
Using exponent rule, a^b\times a^c=a^{b+c}a
b
×a
c
=a
b+c
(\frac{5}{3})^{-4+(-5)}=(\frac{5}{3})^{3x}(
3
5
)
−4+(−5)
=(
3
5
)
3x
(\frac{5}{3})^{-4-5}=(\frac{5}{3})^{3x}(
3
5
)
−4−5
=(
3
5
)
3x
(\frac{5}{3})^{-9}=(\frac{5}{3})^{3x}(
3
5
)
−9
=(
3
5
)
3x
Compare the base,
-9=3x−9=3x
x=-\frac{9}{3}x=−
3
9
x=-3x=−3
therefore the ans is -3 plz mark the brain list
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