Simplify: 84×143×5×3445×73×62 [3 MARKS]

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Simplify: $\frac{8^{4} \times 14^{3} \times 5 \times 3^{4}}{4^{5} \times 7^{3} \times 6^{2}}$ [3 MARKS]

Options:

Answer: Option A
:

Application: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Consider,
$\frac{8^{4} \times 14^{3} \times 5 \times 3^{4}}{4^{5} \times 7^{3} \times 6^{2}}$
$8^{4} = (2^{3})^{4} = 2^{12}$
$14^{3} = (2 \times 7)^{3} = 2^{3} \times 7^{3}$
$4^{5} = (2^{2})^{5} = 2^{10}$
$6^{2} = (2 \times 3)^{2} = 2^{2} \times 3^{2}$
On substituting the values we get:
$\frac{2^{12} \times 2^{3} \times 7^{3} \times 5 \times 3^{4}}{2^{10} \times 7^{3} \times 2^{2} \times 3^{2}}$
$= 2^{12 + 3 - 10 - 2} \times 7^{3 - 3} \times 5 \times 3^{4 - 2}$ [ $∵ \frac{a^{m}}{a^{n}} = a^{m - n}$ ]
$= 2^{3} \times 5 \times 3^{2}$ [ $∵ a^{0} = 1$ ]
$= 8 \times 5 \times 9$
$= 360$

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