Simplify: (2⁵ ÷ 2⁸) × 2⁻⁷

Solution:

Given, the expression is (2⁵ ÷ 2⁸) × 2⁻⁷.

We have to simplify the given expression.

a^m ÷ aⁿ = a^{m - n}

From the given expression,

a = 2

m = 5

n = 8

So, m - n = 5 - 8

= -3

So, 2⁵ ÷ 2⁸ = 2⁻³

Using law of exponents,

a^m × aⁿ = a^{m + n}

From the expression 2⁻³ × 2⁻⁷,

a = 2

m = -3

n = -7

So, m + n = -3 + (-7)

= -3 - 7

= -10

Therefore, (2⁵ ÷ 2⁸) × 2⁻⁷ = 2⁻¹⁰.

✦ Try This: Simplify: (4⁵ ÷ 4⁷) × 4⁻³

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 98(iv)

Summary:

On simplifying (2⁵ ÷ 2⁸) × 2⁻⁷, we get 2⁻¹⁰ using the law of exponents a^m ÷ aⁿ = a^{m - n}

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