Grade 10 Maths · Algebra

Take out a common power

Split powers with the same base and take out the common power (for example 2ˣ⁺¹ + 2ˣ = 2ˣ(2 + 1) = 3 × 2ˣ).

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Exponents Grade 10: More than One TermKevinmathscience

Grade 11 Exponents: Simplifying exponential expressions ADDITION AND SUBTRACTION (FACTORISE!)Miss Martins Maths and Science

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Question 1.1.4 · May/June 2024 · Paper 1 · National (DBE) · 4 marks

1.1 Solve for x:

1.1.4

5^{2 x} - 5^{x} = 0

(4)

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More past paper questions: take out a common power

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3. Question 2.1.2 · June 2024 · Paper 1 · Provincial · 3 marks
2.1 Simplify the following:
2.1.2 $\frac{3 ^{x} - 2. 3 ^{x - 1}}{3 ^{x + 2} + 2. 3 ^{x + 1}}$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Factorise numerator and denominator $= \frac{3 ^{x} ( 1 - 2. 3 ^{- 1} )}{3 ^{x} ( 3 ^{2} + 2.3 )}$
  2 marks · Take out a common power
2. ✓
  Simplify and calculate final answer $= \frac{1 - \frac{2}{3}}{9 + 6}$
  $= \frac{\frac{1}{3}}{15}$
  $= \frac{1}{45}$
  1 mark · Simplify an algebraic fraction
4. Question 1.5.3 · March 2024 · Provincial · 4 marks
1.5 Simplify the following expressions fully:
1.5.3 $\frac{2 ^{x} - 2 ^{x - 2}}{2 ^{x + 1} - 2 ^{x}}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Expand exponents $\frac{2 ^{x} - 2 ^{x} \cdot 2 ^{- 2}}{2 ^{x} \cdot 2 ^{1} - 2 ^{x}}$
  1 mark · Use the laws of exponents
2. ✓
  Factor out common term $\frac{2 ^{x} ( 1 - 2 ^{- 2} )}{2 ^{x} ( 2 - 1 )}$
  2 marks · Take out a common power
3. ✓
  Simplify $1 - \frac{1}{4} = \frac{3}{4}$
  1 mark · Use the laws of exponents
5. Question 1.2.3 · November 2024 · Paper 1 · Provincial · 4 marks
1.2 Simplify the following expressions completely:
1.2.3 $\frac{3 ^{x + 1} - 3 ^{x + 2}}{3 ^{x + 2} + 3 ^{x}}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Factorise numerator and denominator $\frac{3 ^{x} ( 3 ^{1} - 3 ^{2} )}{3 ^{x} ( 3 ^{2} + 1 )}$
  2 marks · Take out a common power
2. ✓
  Simplify the constants $\frac{3 - 9}{9 + 1}$
  $= \frac{- 6}{10}$
  1 mark · Simplify an algebraic fraction
3. ✓
  Final simplified fraction $- \frac{3}{5}$
  1 mark · Simplify an algebraic fraction
6. Question 2.1.5 · March 2025 · Provincial · 5 marks
2.1 Solve for x:
2.1.5 $2^{x + 1} + 2^{x - 1} = 20$ (5)
Show the memo (4 ticks)Memo
1. ✓
  Factorise $2^{x} (2^{1} + 2^{- 1}) = 20$
  2 marks · Take out a common power
2. ✓
  Simplify bracket $2^{x} (2 + \frac{1}{2}) = 20$
  $2^{x} (\frac{5}{2}) = 20$
  1 mark · Use the laws of exponents
3. ✓
  Isolate base $2^{x} = 20 \times \frac{2}{5} = 8$
  $2^{x} = 2^{3}$
  1 mark · Solve a linear equation
4. ✓
  Solve $x = 3$
  1 mark · Solve an exponential equation

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