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Grade 8 Exponents Quiz - 50 Marks

Laws of exponents, roots, order of operations, prime factors and scientific notation — 25 questions, 50 marks

What this quiz covers

grade8_exponents_quiz_50_marks draws its questions at random from a bank of 25 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.

Evaluate \(2^6\).

  1. \(64\)
  2. \(12\)
  3. \(32\)
  4. \(36\)

Answer: \(64\)

\(2^6\) means 2 multiplied by itself 6 times.

\(2\times2\times2\times2\times2\times2 = 64\)

*The exponent is not a multiplier: \(2^6 \neq 2\times 6\).

Simplify, leaving your answer in exponential form: \(3^2 \times 3^4\)

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

Answer: \(3^6\)

Same base, so ADD the exponents: \(a^m \times a^n = a^{m+n}\).

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

*Keep the base as 3 — never multiply the bases.

Simplify: \(a \times b \times a^2 \times b^3\)

  1. \(a^3b^4\)
  2. \(a^2b^3\)
  3. \(a^3b^3\)
  4. \(a^2b^4\)

Answer: \(a^3b^4\)

Group the like bases: \(a \times a^2\) and \(b \times b^3\).

Remember \(a = a^1\) and \(b = b^1\).

\(a^{1+2} = a^3\) and \(b^{1+3} = b^4\)

Simplify: \(x^2 \cdot 2x^3 \cdot 5x^4\)

  1. \(10x^9\)
  2. \(7x^9\)
  3. \(10x^{24}\)
  4. \(7x^{24}\)

Answer: \(10x^9\)

Multiply the coefficients: \(1 \times 2 \times 5 = 10\).

Add the exponents of \(x\): \(2+3+4 = 9\).

Simplify: \(\dfrac{k^8}{k^6}\)

  1. \(k^2\)
  2. \(k^{14}\)
  3. \(k^{48}\)
  4. \(k\)

Answer: \(k^2\)

Same base, so SUBTRACT the exponents: \(a^m \div a^n = a^{m-n}\).

\(k^{8-6} = k^2\)