Laws of exponents
Answers are for parents and teachers.
1
Find (−2)⁵ and −2⁴.
(−2)⁵ = −32; −2⁴ = −16.
2
Simplify 3⁵ × 3⁻² and give the value.
3³ = 27.
3
Find (3/4)⁻² and 10⁻².
(4/3)² = 16/9; 10⁻² = 1/100 = 0.01.
4
Simplify (4ⁿ × 2ⁿ⁺¹) ÷ 8ⁿ.
Write 4ⁿ = 2²ⁿ and 8ⁿ = 2³ⁿ. The exponent is 2n + n + 1 − 3n = 1, so the answer is 2.
5
A cube has edge 2√5 cm. Find its volume.
(2√5)³ = 8 × 5√5 = 40√5 cm³.