Question

Which expression is equivalent to (m^5n/pq^2)^4

Answer 1

$\left( \cfrac{m^5n}{pq^2}\right)^4 = \cfrac{(m^5n)^4}{(pq^2)^4}= \cfrac{m^{20}n^4}{p^4q^8}$

Answer 2

Answer

Find the expression is equivalent to

$(\frac{m^{5}n}{pq^{2}})^{4}$

To prove

As the expression is given in the question as follow .

$=(\frac{m^{5}n}{pq^{2}})^{4}$

By using the exponent properties of the raise a power to a power

$(x^{a})^{b} = x^{ab}$

than the above expression becomes

$=\frac{(m^{5}n)^{4}}{(pq^{2})^{4}}\\ =\frac{(m^{5})^{4}n^{4}}{p^{4}(q^{2})^{4}}$

$=\frac{m^{20}n^{4}}{p^{4}q^{8}}$

Thus the expression is equivalent to

$=(\frac{m^{20}n^{4}}{p^{4}q^{8}})$