I want this answer with full explain
Answers
Answer:
The value of n is 10.
Step-by-step explanation:
Given : 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
Answer:
your answer
Step-by-step explanation
(2/3) ^3 x (2/3)^21 = (2/3) ^3x
(2/3) ^ 3 + 21 = (2/3) ^3x
(2/3) ^24 = (2/3) ^3x
hence,
24 = 3x ( we know that when bases are same powers can be equated)
24/3 = x
8 = x
hence, the required value of x is 8