SIMPLIFY THE FOLLOWING:
(1) 12p4 x 9p3 x 4 DIVIDED BY 6p3 x 8p2 x 27
(2) 3p5 x 10p5 x 25 DIVIDED BY 2p7 x 6p5
KEY:
[1] p = POWER OF
[2] x = MULTIPLIED BY

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Solution

Answer :

Simplify :

1 ) $\frac{12^{4} \times 9^{3} \times 4}{6^{3} \times 8^{2} \times 27}$ , So

$\Rightarrow \frac{{(2 \times 2 \times 3)}^{4} \times {(3 \times 3)}^{3} \times (2 \times 2)}{{(2 \times 3)}^{3} \times {(2 \times 2 \times 2)}^{2} \times (3 \times 3 \times 3)} \Rightarrow \frac{{(2^{2} \times 3)}^{4} \times {(3^{2})}^{3} \times (2^{2})}{{(2 \times 3)}^{3} \times {(2^{3})}^{2} \times (3^{3})} (We know a^{m} \times a^{n} = a^{m + n}) \Rightarrow \frac{2^{8} \times 3^{4} \times 3^{6} \times 2^{2}}{2^{3} \times 3^{3} \times 2^{6} \times 3^{3}} (We know {(a^{m})}^{n} = a^{m \times n}) \Rightarrow \frac{2^{10} \times 3^{10}}{2^{9} \times 3^{6}} \Rightarrow 2^{(10 - 9)} \times 3^{(10 - 6)} (We know \frac{a^{m}}{a^{n}} = a^{m - n}) \Rightarrow 2^{1} \times 3^{4} \Rightarrow 2 \times 3^{4} (Ans)$

2 ) $\frac{3^{5} \times 10^{5} \times 25}{2^{7} \times 6^{5}}$ , So

$\Rightarrow \frac{3^{5} \times {(2 \times 5)}^{5} \times (5 \times 5)}{2^{7} \times {(2 \times 3)}^{5}} \Rightarrow \frac{3^{5} \times 2^{5} \times 5^{5} \times 5^{2}}{2^{7} \times 2^{5} \times 3^{5}} \Rightarrow \frac{3^{5} \times 2^{5} \times 5^{7}}{2^{12} \times 3^{5}} \Rightarrow \frac{3^{(5 - 5)} \times 5^{7}}{2^{(12 - 5)}} \Rightarrow \frac{3^{0} \times 5^{7}}{2^{7}} \Rightarrow 1 \times \frac{5^{7}}{2^{7}} \Rightarrow {(\frac{5}{2})}^{7} (Ans)$

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