Question

if (2÷3)^3×(2÷3)^5=(2÷3)^n_2 then find the value of n​

Answer 1

Answer:

10

Step-by-step explanation:

(2÷3)^3×(2÷3)^5=(2÷3)^n_2

(2÷3)^8=(2÷3)^n_2

n-2=8

n=10

Mark brainliest

Answer 2

The value of n is 10.

$\huge \bold{explanation : - }$

$\bold{ (\frac{2}{3})^3\times (\frac{2}{3})^5=(\frac{2}{3})^{n-2}(32)3×(32)5=(32)n−2}$

$Using \: exponent \: identity, \\  a^b\times a^c=a^{b+c}ab×ac=ab+c \\ (\frac{2}{3})^{3+5}=(\frac{2}{3})^{n-2}(32)3+5=(32)n−2 \\ (\frac{2}{3})^{8}=(\frac{2}{3})^{n-2}(32)8=(32)n−2 \\ Comparing the base, \\ \\ 8=n-28=n−2 \\ n= \: 10 Therefore, \\ \: the \: value \: of \: n \: is \: \: 10$

scroll → to see the attached full