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Express the following in single exponential form: (- 5)⁵ × (-5)

Solution:

Given, (- 5)⁵ × (-5).

We have to express it in a single exponential form.

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

a^m × b^m = (a × b)^m

Now, (-5)⁵ = (-1 × 5)⁵

= (-1)⁵ × (5)⁵

Now, (- 5)⁵ × (-5) = (-1)⁵ × ( 5)⁵ × (-1) × (5)

Considering (- 1)⁵,

We know, (-1)ⁿ = -1, if n = odd number

n = 5, which is a odd number

(-1)⁵ = -1

Considering (5)⁵ × (5),

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

a^m × aⁿ = (a)^{m + n}

Here, a = 5, m = 5 and n = 1

m + n = 5 + 1 = 6

(a)^m+n = (5)⁶

So, (-1)⁵ × ( 5)⁵ × (-1) × (5) = (-1) × (-1) × 5⁶

= 1 × 5⁶

= 5⁶

Therefore, the required value is 5⁶.

✦ Try This: Express the following in single exponential form: (-7)² × (-7)

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

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

Summary:

The single exponential form of (- 5)⁵ × (-5) is 5⁶.

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