Question

find the values of n in each of the following (2/3)¹⁰×{3/2)²}⁵=(2/3)²ⁿ‐²
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Answer 1

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Answer 2

Step-by-step explanation:

Step-by-step explanation:

Given : Expression (\frac{2}{3})^3\times (\frac{2}{3})^5=(\frac{2}{3})^{n-2}(32)3×(32)5=(32)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}(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=10n=10

Therefore, the value of n is 10.

#Learn more

2^n= 512 find the value of n in each of the following