Powers and roots worksheet — GCSE Higher

1.Given that 2⁵ = 32, work out 2⁶.

2.Work out ∛64.

3.Work out 3³ + 2⁴.

4.Work out the value of 6² − 4³.

5.Work out √(4 × 9)

6.4ˣ = 64. Work out the value of x.

7.Work out −(−3)⁴ + (−3)³

8.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

9.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

10.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

11.Simplify ⁴√(16a⁸b¹²)

12.Work out ⁴√16

13.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

14.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

15.Work out ∛(−27) + ∛8