Cambridge IGCSE Maths 0580 Indices Questions

1. (a) Any non-zero number to the power \(0\) is \(1\).
2. (b) \(4^{-2} = \frac{1}{4^2} = \frac{1}{16}\).

Answer: (a) \(1\) (b) \(\frac{1}{16}\)

1. (a) Add the indices: \(a^{7+2} = a^9\)
2. (b) Subtract the indices: \(b^{10-3} = b^7\)
3. (c) Multiply the indices: \(c^{4 \times 2} = c^8\)

Answer: (a) \(a^9\) (b) \(b^7\) (c) \(c^8\)

• B1 (a) 2⁶
• B1 (b) 64

Answer: (a) \(2^6\) (b) \(64\)

• B2 12x⁷ (B1 for 12 or x⁷)

Answer: \(12x^7\)

1. \(3^{-2} \times 3^5 = 3^{-2+5} = 3^3\)
2. \(3^3 = 27\)

Answer: \(27\)

1. (a) \(2^4 = 16\) and \((x^3)^4 = x^{12}\), so \(16x^{12}\).
2. (b) \(12 \div 3 = 4\), \(a^{5-2} = a^3\), \(b^{2-1} = b\), so \(4a^3b\).

Answer: (a) \(16x^{12}\) (b) \(4a^3b\)

• M1 25 = 5² or 1/25 = 5⁻²
• A1 −2

Answer: \(n = -2\)

1. (a) \(\sqrt[3]{64} = 4\), then \(4^2 = 16\).
2. (b) \(27^{\frac{1}{3}} = 3\), and the negative index gives the reciprocal: \(\frac{1}{3}\).

Answer: (a) \(16\) (b) \(\frac{1}{3}\)

1. (a) \(32 = 2^5\), so \(x + 1 = 5\) and \(x = 4\).
2. (b) \(9^x = (3^2)^x = 3^{2x}\), so \(2x = 5\) and \(x = 2.5\).

Answer: (a) \(x = 4\) (b) \(x = 2.5\)

1. The negative index turns the fraction upside down: \(\left(\frac{27}{8}\right)^{\frac{2}{3}}\).
2. Cube root: \(\frac{3}{2}\). Square: \(\frac{9}{4}\).

Answer: \(\frac{9}{4}\)