If x/y = (-2/3)³/(3/5)^–2,find the value of (x/y+y/x)^–¹
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Answer:
Expression (\frac{2}{3})^3\times (\frac{2}{3})^5=(\frac{2}{3})^{n-2}(
3
2
)
3
×(
3
2
)
5
=(
3
2
)
n−2
To find : The value of n in each of the following expression ?
Solution :
Expression (\frac{2}{3})^3\times (\frac{2}{3})^5=(\frac{2}{3})^{n-2}(
3
2
)
3
×(
3
2
)
5
=(
3
2
)
n−2
Using exponent identity, a^b\times a^c=a^{b+c}a
b
×a
c
=a
b+c
(\frac{2}{3})^{3+5}=(\frac{2}{3})^{n-2}(
3
2
)
3+5
=(
3
2
)
n−2
(\frac{2}{3})^{8}=(\frac{2}{3})^{n-2}(
3
2
)
8
=(
3
2
)
n−2
Comparing the base,
8=n-28=n−2
n=10n=10
Therefore, the value of n is 10.
#Learn more
2^n= 512 find the value of n in each of the following
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