Question

Find the value of the following:

 (2⁻¹ × 4⁻¹) ÷ 2⁻²

Answer 1

According to the rules of exponents,

(a^m)ⁿ = a^mn, a^−m = 1/a^m

(2⁻¹ × 4⁻¹) ÷ 2⁻²

= [2⁻¹ × {(2)²}⁻¹] ÷ 2⁻²[Since 4 = 2 × 2 = 2²]

= (2⁻¹ × 2⁻²) ÷ 2⁻² [∵(a^m)ⁿ = a^mn]

= 2⁻³ ÷ 2⁻² [∵a^m × aⁿ = a^{m + n}]

= 2^{−3 + 2} = 2⁻¹

1/2 [∵a^−m = 1/a^m]