Indices worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 32 marks Sheet 1

3 marks
(a)
Simplify \(t^{ 7 } \times t^{ 6 }\)

(b)
Simplify \(t^{ 12 } \div t^{ 4 }\)

(c)
Simplify \((t^{ 2 })^{ 2 }\)
3 marks
(a)
Write down the value of \(5^{0}\)

(b)
Work out \(3^{ -2 }\)

Give your answer as a fraction.

(c)
Write \(\frac{1}{ k^{ 3 } }\) as a power of \(k\)
4 marks
(a)
Simplify fully \(4w^{ 2 } \times 2w^{ 3 }\)

(b)
Simplify fully \(\frac{ 8w^{ 5 } }{ 4w^{ 2 } }\)
2 marks
Simplify fully \(\frac{ (k^{ 5 })^{ 4 } }{ k^{ 5 } }\)
4 marks
(a)
Simplify fully \(6x^{ 4 }y^{ 4 } \times 6x^{ 4 }y^{ 4 }\)

(b)
Simplify fully \(\frac{ 6x^{ 7 }y^{ 4 } }{ 3x^{ 2 }y^{ 2 } }\)
4 marks
(a)
Find the value of \(144^{\frac{1}{2}}\)

(b)
Find the value of \(125^{\frac{1}{3}}\)

(c)
Find the value of \(125^{\frac{2}{3}}\)
3 marks
(a)
Simplify fully \(w^{ 2 } \times w^{ 6 }\)

(b)
Simplify fully \(w^{ 12 } \div w^{ 3 }\)

(c)
Simplify fully \((w^{ 2 })^{ 3 }\)
3 marks
(a)
State the value of \(12^{0}\)

(b)
Work out \(7^{ -3 }\)

Give your answer as a fraction.

(c)
Write \(\frac{1}{ t^{ 4 } }\) as a power of \(t\)
4 marks
(a)
Simplify \(2y^{ 4 } \times 7y^{ 3 }\)

(b)
Simplify \(\frac{ 9y^{ 6 } }{ 3y^{ 4 } }\)
2 marks
Simplify fully \(\frac{ (w^{ 4 })^{ 4 } }{ w^{ 2 } }\)

Answers

(a) \(t^{ 13 }\)
(b) \(t^{ 8 }\)
(c) \(t^{ 4 }\)
(a) \(1\)
(b) \(\frac{1}{ 9 }\)
(c) \(k^{ -3 }\)
(a) \(8w^{ 5 }\)
(b) \(2w^{ 3 }\)
\(k^{ 15 }\)
(a) \(36x^{ 8 }y^{ 8 }\)
(b) \(2x^{ 5 }y^{ 2 }\)
(a) \(12\)
(b) \(5\)
(c) \(25\)
(a) \(w^{ 8 }\)
(b) \(w^{ 9 }\)
(c) \(w^{ 6 }\)
(a) \(1\)
(b) \(\frac{1}{ 343 }\)
(c) \(t^{ -4 }\)
(a) \(14y^{ 7 }\)
(b) \(3y^{ 2 }\)
\(w^{ 14 }\)