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

Question

Simplify:

\frac{8^{4} \times 14^{3} \times 5 \times 3^{4}}{4^{5} \times 7^{3} \times 6^{2}}

[3 MARKS]

Answer:
:
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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