Grade 8 Mathematics

Exponent Laws — Quiz 1

Test your understanding of all seven exponent laws. 15 questions covering multiplication, division, power of a power, zero and negative exponents. Enter your name to begin.

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What this quiz covers

Grade 8 — Exponent Laws Quiz 1 draws its questions at random from a bank of 31 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: \(x^4 \times x^5\)

  1. \(x^{20}\)
  2. \(x^1\)
  3. \(x^9\)
  4. \(2x^9\)

Answer: \(x^9\)

When multiplying powers with the same base, add the exponents.

\(x^4 \times x^5 = x^{4+5}\)

\(= x^9\)

*Law 1: \(a^m \times a^n = a^{m+n}\)

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

  1. \(3^8\)
  2. \(3^6\)
  3. \(9^6\)
  4. \(3^{24}\)

Answer: \(3^6\)

Same base (3), so add the exponents:

\(3^2 \times 3^4 = 3^{2+4} = 3^6\)

*Check: \(3^6 = 729\). Do not multiply the bases together.

Simplify: \(\dfrac{y^8}{y^3}\)

  1. \(y^{24}\)
  2. \(y^{11}\)
  3. \(y^2\)
  4. \(y^5\)

Answer: \(y^5\)

When dividing powers with the same base, subtract the exponents.

\(\dfrac{y^8}{y^3} = y^{8-3}\)

\(= y^5\)

*Law 2: \(\dfrac{a^m}{a^n} = a^{m-n}\)

Simplify: \(\dfrac{2^9}{2^4}\)

Subtract the exponents (same base):

\(\dfrac{2^9}{2^4} = 2^{9-4} = 2^5\)

Calculate \(2^5\):

\(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\)

Simplify: \((a^3)^4\)

  1. \(a^7\)
  2. \(a^{12}\)
  3. \(a^{81}\)
  4. \(a^{34}\)

Answer: \(a^{12}\)

When raising a power to a power, multiply the exponents.

\((a^3)^4 = a^{3 \times 4}\)

\(= a^{12}\)

*Law 3: \((a^m)^n = a^{mn}\)