Question

Simplify and express in exponential form: [3 marks]

$\frac{2^3\times 3^4\times 4}{3\times 32}$

Answer 1

Factors of 32 = 2 × 2 × 2 × 2 × 2 (0.25 Marks)

= 2⁵ (0.25 Marks)

Factors of 4 = 2 × 2 (0.25 Marks)

= 2² (0.25 Marks)

Then,

$\frac{2^3\times 3^4\times 4}{3\times 32}$ (0.5 Marks)

= $\frac{2^3\times 3^4\times 2^2}{3\times 2^5}$ (0.5 Marks)

= $2^{(3+2-5)}\times 3^{4-1}$ (0.5 Marks)

= $2^0\times 3^3=1\times 3^3=3^3$ (0.5 Marks)