Question

Using laws and exponents, simplify and write the answer in exponential form? Thank you ​

Answer 1

Given :

$\dfrac{ {3}^{2} \times {7}^{8} \times {13}^{6} }{ {21}^{2} \times {91}^{3} }$

To find : Simplified form ( in exponential)

Identity used :

$\sf \bullet \: \dfrac{ {a}^{m} }{ {a}^{n} } \: = \: {a}^{m -n} \\ \\ \sf \bullet \: {(a \times b)}^{m} = {a}^{m} \times {b}^{m}$

Solution :

we can write ,

• 21 = 3×7
• 91 = 7×13

$\implies \sf \: \dfrac{ {3}^{2} \times {7}^{8} \times {13}^{6} }{ {21}^{2} \times {91}^{3} } \\ \\ \implies \sf \: \dfrac{ {3}^{2} \times {7}^{8} \times {13}^{6} }{ {(3 \times 7)}^{2} \times {(7 \times 13)}^{3} } \\ \\ \implies \sf \: \dfrac{ {3}^{2} \times {7}^{8} \times {13}^{6} }{ {3 }^{2} \times {7}^{2} \times {7}^{3} \times { 13}^{3} } \\ \\ \implies \sf \: \dfrac{ {3}^{2} }{ {3}^{2} } \times \dfrac{ {7}^{8} }{ {7}^{2} \times {7}^{3} } \times \dfrac{ {13}^{6} }{ {13}^{3} } \\ \\ \implies \sf \: 1 \times {7}^{(8 - 2 - 3)} \times {13}^{(6 - 3)} \\ \\ \implies \: {7}^{3} \times {13}^{3}$

ANSWER : 7³×13³