Grade 10 Maths · Algebra

Solve an equation with rational exponents

Solve an equation with a fraction power by raising both sides to the flipped power (for example x^(2/3) = 4 gives x = 4^(3/2) = 8).

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11) Rational exponent equationsKevinmathscience

Equations with rational exponents: Grade 11 Exponents and EquationsMiss Martins Maths and Science

Rational exponents in equations 1 (mathdou) Grade 11 and olderDou Kleefstra

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Question 2.1 · March 2019 · Provincial · 2 marks

2.1 Solve for x without the use of a calculator:

x^{\frac{3}{4}} = 64

(2)

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More past paper questions: solve an equation with rational exponents

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3. Question 2.2.1 · March 2025 · Provincial · 3 marks
2.2 Solve for $x$ , without using a calculator:
2.2.1 $2 x^{- \frac{1}{3}} = 3$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate the power $x^{- \frac{1}{3}} = \frac{3}{2}$
  1 mark · Solve a linear equation
2. ✓
  Raise both sides to reciprocal power $(x^{- \frac{1}{3}})^{- 3} = (\frac{3}{2})^{- 3}$
  1 mark · Solve an equation with rational exponents
3. ✓
  Final answer $x = (\frac{2}{3})^{3} = \frac{8}{27}$
  1 mark · Solve an equation with rational exponents
4. Question 2.2.1 · June 2024 · Paper 1 · Provincial · 3 marks
2.2 Solve for $x$ WITHOUT using a calculator:
2.2.1 $2 x^{\frac{3}{4}} = 16$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate power $x^{\frac{3}{4}} = 8$
  1 mark · Solve a linear equation
2. ✓
  Raise to reciprocal power $x = 8^{\frac{4}{3}}$
  $x = (38)^{4}$
  1 mark · Solve an equation with rational exponents
3. ✓
  Final answer $x = 2^{4} = 16$
  1 mark · Solve an equation with rational exponents
5. Question 2.1.3 · March 2023 · Provincial · 3 marks
2.1 Solve for x:
2.1.3 $3 x^{\frac{5}{4}} = 96$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate x term $x^{\frac{5}{4}} = 32$
  1 mark · Solve a linear equation
2. ✓
  Apply reciprocal exponent $x = (2^{5})^{\frac{4}{5}}$
  1 mark · Solve an equation with rational exponents
3. ✓
  Simplify $x = 2^{4} = 16$
  1 mark · Solve an equation with rational exponents
6. Question 2.2.3 · March 2020 · Provincial · 3 marks
2.2 Solve for x
2.2.3 $2 - 16 x^{- \frac{3}{2}} = 0$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate x term $16 x^{- \frac{3}{2}} = 2$
  $x^{- \frac{3}{2}} = \frac{2}{16} = \frac{1}{8}$
  1 mark · Solve a linear equation
2. ✓
  Raise both sides to the power $- \frac{2}{3}$ $x = (\frac{1}{8})^{- \frac{2}{3}} = (2^{- 3})^{- \frac{2}{3}}$
  1 mark · Solve an equation with rational exponents
3. ✓
  Answer $x = 2^{2} = 4$
  1 mark · Solve an equation with rational exponents

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