Question

Simplify: (2 * 3 ^ 4 * 2 ^ 3)/(3 ^ 2 * (2 ^ 2) ^ 2)​

Answer 1

The Answer is 9

Step-by-step explanation:

Solve step by step $\frac{2 \times {3}^{4}\times {2}^{3} }{ {3}^{2} \times { ({2}^{2}) }^{2} }$

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

Now we know that when there are same bases, break the fraction in such a way that the fraction would have same bases:

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

Now when we have same bases as numerator and denominator in fraction, subtract the smaller exponential number from higher one :

$= 2 \times {3}^{(4 - 2)} \times {2}^{(3 - 4)}$

$= {2}^{1} \times {3}^{2} \times {2}^{ - 1}$

$= 2 \times 3 \times 3 \times \frac{1}{2}$

$= 3 \times 3$

$= 9$

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