Grade 10 Maths · Algebra

Change the base of a power

Write a number as a power of a smaller base so the powers can be compared or combined (for example 8ˣ = (2³)ˣ = 2³ˣ).

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Exponents Grade 10: Change to prime numberKevinmathscience

Exponents Grade 10: Prime Number Exam QuestionKevinmathscience

Exponential Equations grade 10Kevinmathscience

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Question 3.3 · November 2024 · Paper 1 · National (DBE) · 4 marks

A circle with radius

6

cm is drawn. A second, smaller circle is drawn through the centre of the first circle and also touches the first circle internally, as shown in the diagram. A third, smaller circle is drawn through the centre of the second circle and touches the second circle internally. The process of drawing circles continues and forms a geometric pattern. Diagram for this question

3.3 Which circle has a diameter of

\frac{3}{128}

cm?(4)

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

More past paper questions: change the base of a power

Work each one out first, then open the memo and check every tick.

3. Question 1.5.2 · March 2025 · Provincial · 2 marks
1.5 If $2^{x} = 3$ , evaluate:
1.5.2 $8^{x}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Rewrite base $(2^{3})^{x} = (2^{x})^{3}$
  1 mark · Change the base of a power
2. ✓
  Substitute and evaluate $(3)^{3} = 27$
  1 mark · Use the laws of exponents
4. Question 1.4.3 · March 2025 · Provincial · 2 marks
1.4 Simplify fully:
1.4.3 $\frac{3 ^{500} \cdot 7 ^{500} \cdot 2 ^{502}}{4 2 ^{500}}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Break down denominator bases $\frac{3 ^{500} \cdot 7 ^{500} \cdot 2 ^{502}}{( 3 \cdot 7 \cdot 2 ) ^{500}}$
  $\frac{3 ^{500} \cdot 7 ^{500} \cdot 2 ^{502}}{3 ^{500} \cdot 7 ^{500} \cdot 2 ^{500}}$
  1 mark · Change the base of a power
2. ✓
  Simplify using exponent laws $2^{502 - 500}$
  $2^{2} = 4$
  1 mark · Use the laws of exponents
5. Question 3.1.3 · June 2024 · Paper 1 · Provincial · 4 marks
3.1 Solve for x:
3.1.3 $16. 2^{x - 1} = (0, 5)^{x - 4}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Convert to prime bases $2^{4} . 2^{x - 1} = (2^{- 1})^{x - 4}$
  2 marks · Change the base of a power
2. ✓
  Simplify exponents $2^{x + 3} = 2^{- x + 4}$
  1 mark · Use the laws of exponents
3. ✓
  Equate exponents and solve $x + 3 = - x + 4$
  $2 x = 1$
  $x = \frac{1}{2}$
  1 mark · Solve an exponential equation
6. Question 2.1.1 · November 2024 · Paper 1 · Provincial · 4 marks
2.1 Solve for $x$ :
2.1.1 $2. 3^{2 x} = 18$ (4)
Show the memo (2 ticks)Memo
1. ✓
  Isolate the power $3^{2 x} = 9$
  $3^{2 x} = 3^{2}$
  2 marks · Change the base of a power
2. ✓
  Equate exponents and solve $2 x = 2$
  $x = 1$
  2 marks · Solve an exponential equation

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