The
value
es
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Answer:
Step-by-step explanation:
Given : Expression (\frac{3}{4})^6\times (\frac{16}{9})^5=(\frac{4}{3})^{x+2}(
4
3
)
6
×(
9
16
)
5
=(
3
4
)
x+2
To find : The value of x ?
Solution :
Re-write the expression as,
(\frac{4}{3})^{-6}\times (\frac{4^2}{3^2})^5=(\frac{4}{3})^{x+2}(
3
4
)
−6
×(
3
2
4
2
)
5
=(
3
4
)
x+2
(\frac{4}{3})^{-6}\times (\frac{4}{3})^{10}=(\frac{4}{3})^{x+2}(
3
4
)
−6
×(
3
4
)
10
=(
3
4
)
x+2
Using exponential property, a^b\times a^c=a^{b+c}a
b
×a
c
=a
b+c
(\frac{4}{3})^{-6+10}=(\frac{4}{3})^{x+2}(
3
4
)
−6+10
=(
3
4
)
x+2
(\frac{4}{3})^{4}=(\frac{4}{3})^{x+2}(
3
4
)
4
=(
3
4
)
x+2
Comparing the base,
4=x+24=x+2
x=2x=2
Therefore, the value of x is 2.
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