Maths Library

Exponents and Exponent Rules: Grade 8 math

Students apply laws of indices to simplify expressions involving powers with common bases. The exercises cover multiplication, division, powers of powers, and negative or fractional exponents.

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What this covers

Exponents and Exponent Rules is taught in Grade 8 (age 13 to 14) as a topic to introduce. It sits in the Number strand.

Worked example

Simplify (x^5 × x^3) ÷ x^2.

  1. Apply the product rule to the numerator: x^(5+3) = x^8
  2. Apply the quotient rule: x^(8-2) = x^6
  3. The simplified result is x^6

Answer: x^6

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Product and quotient laws with positive integer indices on a single variable
  2. Power of a power rule and zero index (e.g. (a^3)^2, b^0)
  3. Expressions with coefficients and multiple variables (e.g. 3a^2 × 4a^3)
  4. Negative integer indices (e.g. x^-2 = 1/x^2) and numerical evaluations
  5. Fractional indices and combinations of roots and powers (e.g. 27^(23))

Common mistakes

  • Multiplying the powers instead of adding them when multiplying bases (e.g. x^2 * x^3 = x^6)
  • Applying the power to the coefficient without brackets (e.g. treating 2x^3 as (2x)^3)

Curriculum links

Indicative matches to Common Core State Standards. Check wording and codes against the official document.

  • 8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Exponents and Exponent Rules

Grade 8 math

Qs
6
Marks
6
NameDateScore / 6
1.
Work out 22.
[1]
2.
Work out 32.
[1]
3.
Work out 22.
[1]
4.
Work out 22.
[1]
5.
Work out 22.
[1]
6.
Work out 53.
[1]

Answer key

  1. 42 × 2 = 4
  2. 93 × 3 = 9
  3. 42 × 2 = 4
  4. 42 × 2 = 4
  5. 42 × 2 = 4
  6. 1255 × 5 × 5 = 125