Grade 10 Maths · Algebra · Paper 1

Exponents Grade 10

Real Exponents past paper questions and answers from 2022 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 41 past paper questions
skills: 4 skills
videos: 4 videos

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Question 1.8 · March 2022 · Provincial · 2 marks

Four options are provided as possible answers to the following questions. Choose the correct option.

1.8 If it is given that

y^{5} = 50

and

x^{2} = 10

, determine the value of

y^{10} x^{- 2}

.(2)

A 5
B 25
C 50
D 250

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Exponents skills

Each skill is one thing a memo gives a tick for. Tap one for its own questions, notes and videos.

More Exponents Grade 10 questions and answers

Try each one on paper before you open the memo.

4. Question 1.3.4 · March 2025 · Provincial · 4 marks
1.3 Simplify the following fully:
1.3.4 $\frac{1 0 ^{2 x + 3} \cdot 4 ^{1 - x}}{2 5 ^{2 + x}}$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Convert to prime bases $\frac{( 2 \cdot 5 ) ^{2 x + 3} \cdot ( 2 ^{2} ) ^{1 - x}}{( 5 ^{2} ) ^{2 + x}}$
  $= \frac{2 ^{2 x + 3} \cdot 5 ^{2 x + 3} \cdot 2 ^{2 - 2 x}}{5 ^{4 + 2 x}}$
  1 mark · Change the base of a power
2. ✓
  Group bases $2^{2 x + 3 + 2 - 2 x} \cdot 5^{2 x + 3 - (4 + 2 x)}$
  1 mark · Use the laws of exponents
3. ✓
  Simplify exponents $2^{5} \cdot 5^{- 1}$
  1 mark · Use the laws of exponents
4. ✓
  Final Answer $\frac{32}{5}$
  1 mark · Use the laws of exponents
5. Question 1.2.1 · November 2024 · Paper 1 · Provincial · 2 marks
1.2 Simplify the following expressions completely:
1.2.1 $2 7^{\frac{2}{3}}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Write base as power of 3 $(3^{3})^{\frac{2}{3}}$
  1 mark · Change the base of a power
2. ✓
  Simplify exponents $3^{2} = 9$
  1 mark · Use the laws of exponents
6. 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
7. Question 2.1.3 · March 2024 · Provincial · 3 marks
2.1 Solve for $x$ :
2.1.3 $2^{3 x - 1} = 64$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Express 64 as base 2 $2^{3 x - 1} = 2^{6}$
  1 mark · Change the base of a power
2. ✓
  Equate exponents $3 x - 1 = 6$
  1 mark · Solve an exponential equation
3. ✓
  Solve for x $3 x = 7 ⟹ x = \frac{7}{3}$
  1 mark · Solve an exponential equation
8. Question 1.3.2 · March 2023 · Provincial · 4 marks
1.3 Simplify completely:
1.3.2 $\frac{4 ^{2 y - 1} \cdot 9 ^{y + 1}}{1 8 ^{y} \cdot 8 ^{y - 1}}$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Convert to prime bases $\frac{( 2 ^{2} ) ^{2 y - 1} \cdot ( 3 ^{2} ) ^{y + 1}}{( 2 \cdot 3 ^{2} ) ^{y} \cdot ( 2 ^{3} ) ^{y - 1}}$
  1 mark · Change the base of a power
2. ✓
  Simplify exponents $\frac{2 ^{4 y - 2} \cdot 3 ^{2 y + 2}}{2 ^{y} \cdot 3 ^{2 y} \cdot 2 ^{3 y - 3}}$
  1 mark · Use the laws of exponents
3. ✓
  $2^{1} \cdot 3^{2}$ $2^{4 y - 2 - y - 3 y + 3} \cdot 3^{2 y + 2 - 2 y} = 2^{1} \cdot 3^{2}$
  1 mark · Use the laws of exponents
4. ✓
  Answer $= 18$
  1 mark · Use the laws of exponents
9. Question 2.1.3 · March 2023 · Provincial · 3 marks
2.1 Solve for x:
2.1.3 $(\frac{1}{3})^{x - 1} = 27$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Convert to base 3 $(3^{- 1})^{x - 1} = 3^{3}$
  $3^{- x + 1} = 3^{3}$
  1 mark · Change the base of a power
2. ✓
  Equate exponents $- x + 1 = 3$
  1 mark · Solve an exponential equation
3. ✓
  Solve for x $- x = 2$
  $x = - 2$
  1 mark · Solve an exponential equation
10. Question 3.1.2 · March 2022 · Provincial · 2 marks
3.1 Solve for x:
3.1.2 $3^{x} = 1$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Write 1 as base 3 $3^{x} = 3^{0}$
  1 mark · Change the base of a power
2. ✓
  Solve for exponent $x = 0$
  1 mark · Solve an exponential equation

Exponents Grade 10 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Exponents Grade 8 | All Laws CombinedKevinmathscience

Exponents Grade 10: Change to prime numberKevinmathscience

Exponents Grade 10: More than One TermKevinmathscience

Grade 11 Exponents: Rational exponents | Writing roots as powers with rational exponentsMiss Martins Maths and Science

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