Question

(2/9)3×(2/9)6=(2/9)2m-1

Answer 1

(2/9)^3 ×(2/9)^6 = (2/9)^(2m-1)
comparing quantity
3+6 =2m -1
3+6+1=2m
10/2 = m
m = 5

Answer 2

The value of m is 5.

Given,

$(\frac{2}{9})^3 \times (\frac{2}{9})^6 = (\frac{2}{9})^{2m-1}$

To Find,

the value of m

Solution,

This problem could be solved using a very simple method.

We use the properties of exponents to solve this question.

We have been given the following relationship:

$(\frac{2}{9})^3 \times (\frac{2}{9})^6 = (\frac{2}{9})^{2m-1}$

Let the above equation be equation (1)

We have to find the value of m in the given mathematical relation.

We make use of the following property of exponents to solve the rest of this problem:

$a^m \times a^n = a^{m+n}$

By applying this property in equation (1), we can simplify as follows:

$\implies (\frac{2}{9})^{3+6} = (\frac{2}{9})^{2m-1}\\\\\implies (\frac{2}{9})^9 = (\frac{2}{9})^{2m-1}$

From this, we can obtain the following linear relationship for m:

$\implies 2m-1 = 9\\\\\implies 2m = 10\\\\\implies m = 5$

Therefore, the required value of m is 5.

Read more:

1. https://brainly.in/question/35592912

2 https://brainly.in/question/34644549

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