Question

Solve this question

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


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Answer 1

Required Answer:-

Question:-

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

Solution:-

Factors Of 4 = 2 × 2 = 2²

Factors of 32 = 2 × 2 × 2 × 2 × 2 = 2⁵

Now,

$\dfrac{ {2}^{3} \times {3}^{4} \times {2}^{2} }{3 \times {2}^{5} }$

Law of Exponents To Be used:-

$\sf{ [(a^m × a^n = {a}^{m+n} )] }$

Now,

$\dfrac{ {2}^{3 + 2} \times {3}^{4} }{3 \times {2}^{5} }$

= $\dfrac{{\cancel {2}^{5}} \times {3}^{4} }{3 \times {\cancel {2}^{5}} }$

= 2⁵ is Cancelled By Other 2⁵

= $\dfrac{ {3}^{4} }{3}$

Now Take Factors of 3⁴ = 3 × 3× 3× 3 = 81

$\dfrac{81}{3} = \dfrac{27}{1 } = {3}^{3}$

Hence, Answer of The Question is 3³