Express (2⁵ ÷ 2⁸) × 2⁻⁷ as a power of a rational number with negative exponent.

Solution:

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

We have to express the given term as a power of a rational number with a negative exponent.

Using law of exponents,

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: Express (3⁶ ÷ 3⁸) × 3⁻⁷ as a power of a rational number with negative exponent.

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

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 96(b)

Express (2⁵ ÷ 2⁸) × 2⁻⁷ as a power of a rational number with negative exponent.

Summary:

On expressing (2⁵ ÷ 2⁸) × 2⁻⁷ as a power of a rational number with negative exponent, we get 2^-10.

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☛ Related Questions:

• Find the product of the cube of (-2) and the square of (+4)
• Simplify: (1/4)⁻² + (1/2)⁻² + (1/3)⁻²
• Simplify: [(-2/3)⁻²]³ × (1/3)⁻⁴ × 3⁻¹ × 1/6