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

Find the expression is equivalent to

`((m^(5)n)/(pq^(2)))^(4)`

To prove

As the expression is given in the question as follow .

`=((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

`=((m^(5)n)^(4))/((pq^(2))^(4))\\ =((m^(5))^(4)n^(4))/(p^(4)(q^(2))^(4))`

`=(m^(20)n^(4))/(p^(4)q^(8))`

Thus the expression is equivalent to

`=((m^(20)n^(4))/(p^(4)q^(8)))`