Express the following in single exponential form: 2⁴ × 4²

Solution:

Given, 2⁴ × 4²

We have to express it in a single exponential form.

4 = (2)²

So, (4)² = (2²)²

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

(a^m)ⁿ = (a)^mn

Considering (2²)²,

Here, a = 2, m = 2 and n = 2

= (2)^{2 × 2}

= 2⁴

So, 2⁴ × 4² = 2⁴ × 2⁴

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

a^m × aⁿ = (a)^{m + n}

Here, a = 2, m = 4 and n = 4

m + n = 4 + 4 = 8

(a)^m+n = (2)⁸

Therefore, the required value is 2⁸.

✦ Try This: Express the following in single exponential form: 3⁴ × 5²

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

NCERT Exemplar Class 7 Maths Chapter 11 Problem 81 (b)

Express the following in single exponential form: 2⁴ × 4²

Summary:

The single exponential form of 2⁴ × 4² is 2⁸.

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