Find m so that (2/9)³ × (2/9)⁶ = (2/9)^{2m - 1}

Solution:

Given, (2/9)³ × (2/9)⁶ = (2/9)^{2m - 1}.

We have to find the value of m.

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

a^m × aⁿ = a^m+n

Here, a = 2/9, m = 3 and n = 6

m + n = 3 + 6 = 9

a^m+n = (2/9)⁹

So, (2/9)³ × (2/9)⁶ = (2/9)⁹

Now, (2/9)⁹ = (2/9)^{2m - 1}

The bases are equal.

On equating the powers,

2m - 1 = 9

2m = 9 + 1

2m = 10

m = 10/2

m = 5

Therefore, the value of m is 5.

✦ Try This: Find m so that (7/11)⁴ × (7/11)⁶ = (7/11)^m-1

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 13

NCERT Exemplar Class 7 Maths Chapter 11 Problem 69

Find m so that (2/9)³ × (2/9)⁶ = (2/9)^{2m - 1}

Summary:

The value of m = 5, so that (2/9)³ × (2/9)⁶ = (2/9)^{2m - 1}

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