Question

Simplify The Given question below

Answer 1

Answer

In the question, we are given with a fraction containing the exponential numbers. The given fraction is,

$\sf \dashrightarrow \dfrac{{3}^{ - 5} \times {10}^{ - 5} \times 125}{{5}^{ - 7} \times {6}^{ - 5}}$

We know that, all the numbers given should be in an exponential format. So

$\sf \dashrightarrow \dfrac{{3}^{ - 5} \times {10}^{ - 5} \times {5}^{3}}{{5}^{ - 7} \times {6}^{ - 5}}$

As we know that, the powers of numbers shouldn't be in negative format. So, we can change them into positive by changing the numbers as in numerator and denominator.

$\sf \dashrightarrow \dfrac{{5}^{7} \times {6}^{5}}{{3}^{5} \times {10}^{5} \times {5}^{ - 3}}$

$\sf \dashrightarrow \dfrac{{5}^{7} \times {(2 \times 3)}^{5}}{{3}^{5} \times {(2 \times 5)}^{5} \times {5}^{ - 3}}$

$\sf \dashrightarrow \dfrac{{5}^{7} \times {2}^{5} \times {2}^{5}}{{3}^{5} \times {2}^{5} \times {5}^{5} \times {5}^{ - 3}}$

$\sf \dashrightarrow \dfrac{({5}^{7} \div {5}^{5} \div {5}^{ - 3}) \times ({2}^{5} \times {2}^{5} \div {2}^{5})}{{3}^{5}}$

$\sf \dashrightarrow \dfrac{({5}^{7 - 5 + 3}) \times ({2}^{5 + 5 - 5})}{{3}^{5}}$

$\sf \dashrightarrow \dfrac{{5}^{5} \times {2}^{5}}{{3}^{5}}$

$\sf \dashrightarrow \dfrac{{(5 \times 2)}^{5}}{{3}^{5}}$

$\sf \dashrightarrow \dfrac{{10}^{5}}{{3}^{5}}$

$\sf \dashrightarrow \bigg( \dfrac{10}{3} \bigg)^{5}$

Hence, the answer is (10/3)⁵.