Indices, Powers & Roots — Year 8 Practice Questions
Work through these Year 8 practice questions on indices, powers and roots. Try each one before revealing the worked solution.
Questions
Write 2 × 2 × 2 × 2 × 2 using index notation, then evaluate it.
Work out 7².
Find ∛64.
Between which two whole numbers does √50 lie?
Simplify 3⁴ × 3². Leave your answer in index form.
Simplify 5⁷ ÷ 5³. Leave your answer in index form.
Work out the value of 9⁰ + 2³.
A square has an area of 81 cm². Find the length of one side.
Answers & Worked Solutions
Question 1 Solution
Step 1: There are five 2s multiplied together, so it is 2⁵.
Step 2: 2⁵ = 32.
Answer: 2⁵ = 32
Question 2 Solution
Step 1: 7² means 7 × 7.
Step 2: 7 × 7 = 49.
Answer: 49
Question 3 Solution
Step 1: You need the number that cubes to 64.
Step 2: 4³ = 64, so ∛64 = 4.
Answer: 4
Question 4 Solution
Step 1: 7² = 49 and 8² = 64.
Step 2: 50 is between 49 and 64, so √50 is between 7 and 8.
Answer: 7 and 8
Question 5 Solution
Step 1: Multiplying powers of the same base means adding the indices.
Step 2: 4 + 2 = 6, so the answer is 3⁶.
Answer: 3⁶
Question 6 Solution
Step 1: Dividing powers of the same base means subtracting the indices.
Step 2: 7 − 3 = 4, so the answer is 5⁴.
Answer: 5⁴
Question 7 Solution
Step 1: 9⁰ = 1 (any non-zero number to the power 0 is 1).
Step 2: 2³ = 8, so 1 + 8 = 9.
Answer: 9
Question 8 Solution
Step 1: The side length is the square root of the area.
Step 2: √81 = 9, so each side is 9 cm.
Answer: 9 cm
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