Grade 8 Mathematics

Laws of Exponents Quiz

15 marks | random draw from 30 questions | worked solutions included

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This quiz tests product, quotient, power, zero and negative exponent laws.

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What this quiz covers

Grade 8 Laws of Exponents Quiz draws its questions at random from a bank of 30 questions, with full worked solutions for every one.

Worked examples

A few of the question types, with full solutions, so you know what to expect.

Simplify \(x^3 \times x^5\).

  1. \(x^8\)
  2. \(x^{15}\)
  3. \(2x^8\)
  4. \(x^2\)

Answer: \(x^8\)

Use the product law: \(a^m \times a^n=a^{m+n}\).

\(x^3 \times x^5=x^{3+5}=x^8\)

Simplify \(a^2 \times a^7\).

  1. \(a^9\)
  2. \(a^{14}\)
  3. \(2a^9\)
  4. \(a^5\)

Answer: \(a^9\)

Same base, so add exponents.

\(a^2 \times a^7=a^{2+7}=a^9\)

Simplify \(4^2 \times 4^3\).

  1. \(4^5\)
  2. \(4^6\)
  3. \(16^5\)
  4. \(4^1\)

Answer: \(4^5\)

The base is 4 in both factors.

\(4^2 \times 4^3=4^{2+3}=4^5\)

Simplify \(y \times y^6\).

  1. \(y^7\)
  2. \(y^6\)
  3. \(y^{12}\)
  4. \(2y^6\)

Answer: \(y^7\)

Remember \(y=y^1\).

\(y^1 \times y^6=y^{1+6}=y^7\)

Simplify \(p^4 \times p^4\).

  1. \(p^8\)
  2. \(p^{16}\)
  3. \(2p^4\)
  4. \(p^0\)

Answer: \(p^8\)

Same base, add the exponents.

\(p^4 \times p^4=p^{4+4}=p^8\)