Question

pls solve
for question see the image

Answer 1

★ How to do :-

Here, we are given with the equation in which the concept of exponents has been used. The other formulas used in calculation of this question is the formulas known as Laws of Exponents. There are five laws of exponents in which they should be used in this calculation. The composite numbers given in this equation should be rewritten as the powers of prime numbers. So, let's solve!!

$\:$

➤ Solution :-

${\tt \leadsto \bigg(\dfrac{{3}^{4} \times {12}^{3} \times 36}{ {2}^{5} \times {6}^{3}}\bigg) \times {2}^{6}}$

${\tt \leadsto \bigg(\dfrac{{3}^{4} \times ({3}^{1} \times {2}^{2} {)}^{3} \times {2}^{2} \times {3}^{2}}{ {2}^{5} \times (3 \times 2 {)}^{3}}\bigg) \times {2}^{6}}$

${\tt \leadsto \bigg(\dfrac{{3}^{4} \times {3}^{1 \times 3} \times {2}^{2 \times 3} \times {2}^{2} \times {3}^{2}}{{2}^{5} \times {3}^{3} \times {2}^{3}}\bigg) \times {2}^{6}}$

${\tt \leadsto \bigg(\dfrac{{3}^{4} \times {3}^{3} \times {2}^{6} \times {2}^{2} \times {3}^{2}}{{2}^{5} \times {3}^{3} \times {2}^{3}}\bigg) \times {2}^{6}}$

${\tt \leadsto \bigg(\dfrac{{3}^{4 + 3 + 2} \times {2}^{6 + 2}}{{2}^{5 + 3} \times {3}^{3}}\bigg) \times {2}^{6}}$

${\tt \leadsto \bigg(\dfrac{{3}^{9} \times {2}^{8}}{{2}^{8} \times {3}^{3}}\bigg) \times {2}^{6}}$

${\tt \leadsto \bigg({3}^{9 - 3} \times {2}^{8 - 8} \bigg) \times {2}^{6}}$

${\tt \leadsto {3}^{6} \times {2}^{0} \times {2}^{6}}$

${\tt \leadsto {3}^{6} \times {2}^{6} = (3 \times 2 {)}^{6}}$

${\tt \leadsto {6}^{6} = \boxed{ \tt 46656}}$

$\Huge\therefore$ The answer of this equation is 46656.

━━━━━━━━━━━━━━━━━━━━━━

$\dashrightarrow$ Some related equations :-

${\sf \longrightarrow {a}^{m} \times {a}^{n} = {a}^{m + n}}$

${\sf \longrightarrow {a}^{m} \div {a}^{n} = {a}^{m - n}}$

${\sf \longrightarrow ({a}^{m} {)}^{n} = {a}^{m \times n}}$

${\sf \longrightarrow {a}^{ - 1} = \dfrac{1}{ {a}^{1}}}$

${\sf \longrightarrow {a}^{0} = 1}$