Evaluate (25 × 4-2) ÷ (2-3 × 26)

Analyze the question

The powers lost their formatting when the question was copied. It should read:

(2⁵ × 4⁻²) ÷ (2⁻³ × 2⁶)

This reading gives one of the listed options, so it is the intended one.

Concept

Use the laws of indices:

• aᵐ × aⁿ = aᵐ⁺ⁿ
• aᵐ ÷ aⁿ = aᵐ⁻ⁿ
• Write every number with the same base. Here 4 = 2², so 4⁻² = 2⁻⁴.

Solution

Numerator: 2⁵ × 4⁻² = 2⁵ × 2⁻⁴ = 2⁵⁻⁴ = 2¹ = 2

Denominator: 2⁻³ × 2⁶ = 2⁻³⁺⁶ = 2³ = 8

Divide: 2 ÷ 8 = 2/8 = 1/4

Answer

Tip

Convert every number to the same base first (4 = 2², 8 = 2³, and so on). After that, you only add and subtract the powers.