Solve power equations

CAIE P2 2004 November Q2

3 marks Moderate -0.8

2 Solve the equation \(x ^ { 3.9 } = 11 x ^ { 3.2 }\), where \(x \neq 0\).

OCR C1 2006 January Q1

4 marks Easy -1.8

1 Solve the equations

1. \(x ^ { \frac { 1 } { 3 } } = 2\),
2. \(10 ^ { \prime } = 1\),
3. \(\left( y ^ { - 2 } \right) ^ { 2 } = \frac { 1 } { 81 }\).

OCR C1 2007 January Q4

5 marks Moderate -0.5

4 Solve the equation \(x ^ { \frac { 2 } { 3 } } + 3 x ^ { \frac { 1 } { 3 } } - 10 = 0\).

OCR C1 2008 January Q4

6 marks Easy -1.2

4 Solve the equations

1. \(10 ^ { p } = 0.1\),
2. \(\left( 25 k ^ { 2 } \right) ^ { \frac { 1 } { 2 } } = 15\),
3. \(t ^ { - \frac { 1 } { 3 } } = \frac { 1 } { 2 }\).

OCR MEI C1 Q9

5 marks Easy -1.2

9

1. Simplify \(\frac { 2 ^ { 6 } } { 8 ^ { 2 \frac { 1 } { 2 } } \times 2 ^ { - \frac { 1 } { 2 } } }\)
2. Solve the equation \(x ^ { - \frac { 1 } { 3 } } = 8\).

OCR C1 Q4

6 marks Easy -1.2

4. (i) Evaluate $$\left( 36 ^ { \frac { 1 } { 2 } } + 16 ^ { \frac { 1 } { 4 } } \right) ^ { \frac { 1 } { 3 } }$$ (ii) Solve the equation $$3 x ^ { - \frac { 1 } { 2 } } - 4 = 0 .$$

OCR C1 Q6

7 marks Moderate -0.3

6. $$f ( x ) = x ^ { \frac { 3 } { 2 } } - 8 x ^ { - \frac { 1 } { 2 } }$$

1. Evaluate \(\mathrm { f } ( 3 )\), giving your answer in its simplest form with a rational denominator.
2. Solve the equation \(\mathrm { f } ( x ) = 0\), giving your answers in the form \(k \sqrt { 2 }\).

OCR C1 2015 June Q4

5 marks Moderate -0.3

4 Solve the equation \(x ^ { \frac { 2 } { 3 } } - x ^ { \frac { 1 } { 3 } } - 6 = 0\).

OCR MEI AS Paper 2 2019 June Q1

3 marks Easy -1.2

1 Solve the equation \(4 x ^ { - \frac { 1 } { 2 } } = 7\), giving your answer as a fraction in its lowest terms.

Edexcel C1 Q6

7 marks Moderate -0.3

6. $$f ( x ) = x ^ { \frac { 3 } { 2 } } - 8 x ^ { - \frac { 1 } { 2 } } .$$

1. Evaluate f(3), giving your answer in its simplest form with a rational denominator.
2. Solve the equation \(\mathrm { f } ( x ) = 0\), giving your answers in the form \(k \sqrt { 2 }\).

Edexcel C1 Q4

6 marks Easy -1.3

1. (a) Evaluate

$$\left( 36 ^ { \frac { 1 } { 2 } } + 16 ^ { \frac { 1 } { 4 } } \right) ^ { \frac { 1 } { 3 } }$$ (b) Solve the equation $$3 x ^ { - \frac { 1 } { 2 } } - 4 = 0 .$$

Pre-U Pre-U 9794/2 2018 June Q4

12 marks Moderate -0.3

4 Solve the equation \(x + 2 \sqrt { x } - 6 = 0\), giving your answer in the form \(x = c + d \sqrt { 7 }\) where \(c\) and \(d\) are integers.

OCR C1 2013 January Q2

6 marks Easy -1.3

Solve the equations

1. \(3^n = 1\), [1]
2. \(t^{-3} = 64\), [2]
3. \((8p^6)^{\frac{1}{3}} = 8\). [3]

OCR MEI C1 Q2

3 marks Easy -1.2

Make \(r\) the subject of \(V = \frac{4}{3}\pi r^3\). [3]

OCR MEI C1 2006 January Q5

4 marks Moderate -0.8

Make \(C\) the subject of the formula \(P = \frac{C}{C + 4}\). [4]

OCR MEI C1 2006 June Q1

3 marks Easy -1.2

The volume of a cone is given by the formula \(V = \frac{1}{3}\pi r^2 h\). Make \(r\) the subject of this formula. [3]

OCR MEI C1 2009 June Q2

3 marks Easy -1.8

Make \(a\) the subject of the formula \(s = ut + \frac{1}{2}at^2\). [3]

OCR MEI C1 2010 June Q3

3 marks Easy -1.2

Make \(y\) the subject of the formula \(a = \frac{\sqrt{y} - 5}{c}\). [3]

Edexcel C1 Q3

4 marks Easy -1.3

1. Solve the equation $$x^{\frac{3}{2}} = 27.$$ [2]
2. Express \((2\frac{1}{4})^{-\frac{3}{2}}\) as an exact fraction in its simplest form. [2]

OCR C1 Q3

4 marks Easy -1.3

1. Solve the equation $$x^{\frac{3}{2}} = 27.$$ [2]
2. Express \((2\frac{1}{4})^{-\frac{3}{2}}\) as an exact fraction in its simplest form. [2]

OCR MEI C1 Q1

2 marks Easy -1.8

Make \(r\) the subject of the formula \(A = \pi r^2(x+y)\), where \(r > 0\). [2]

OCR MEI C1 Q4

4 marks Moderate -0.5

Make \(a\) the subject of \(3(a + 4) = ac + 5f\). [4]

WJEC Unit 1 2024 June Q6

7 marks Moderate -0.8

1. Find the exact value of \(x\) that satisfies the equation $$\frac{7x^{\frac{5}{4}}}{x^{\frac{1}{2}}} = \sqrt{147}.$$ [4]
2. Show that \(\frac{(8x-18)}{(2\sqrt{x}-3)}\), where \(x \neq \frac{9}{4}\), may be written as \(2(2\sqrt{x}+3)\). [3]