Question Type 9: Summarizing laws of exponents Exercises

Question 1

Solve for $x$ : $2^{x} \cdot 4^{x-2} = 32$ [3 marks]

[3]

Question 2

Simplify $\dfrac{5^0 + 5^1}{5^2}$

[2]

Question 3

Simplify the following expression.

Simplify $\dfrac{3^4 \cdot 3^{-2}}{3^1}$

[2]

Question 4

Expand and simplify $(x^{2} y^{-1})^{-2} \times x^{3}$

[3]

Question 5

Simplify $\dfrac{16^{x+1}}{8^x}$ and express the result as a power of 2

[3]

Question 6

Simplify $\left(\dfrac{2^5}{2^3}\right)^2$

[2]

Question 7

Simplify $\left(\dfrac{a^3 b^{-2}}{a^{-1} b^4}\right)^{2}$

[3]

Question 8

Solve for $x$ : $4^{2x-1} = 8^{x+2}$

[3]

Question 9

Solve for $x$ : $(\frac{1}{3})^x = 9^{x+1}$

[3]

Question 10

Simplify $(-2)^3 \cdot 4^{-2}$

[3]

Question 11

Solve for $x$ : $5^{2x-3} = 125^{x+\frac{1}{2}}$

[5]

Question 12

Simplify $9^{\frac{3}{2}} \cdot 27^{-\frac{1}{3}}$

[3]