Question

PLEASE HELP! WILL GIVE BRAINLIEST!!!
Which expression is equivalent to $(p^{10}r^{-5})\frac{1}{5}$?

​ A. 1pr ​

​B. 1p2r ​

C.​ p2r​

D.​ p2r ​

Answer 1

When an exponent is multiplied directly into another exponent, you multiply the exponents.

For example:

$(x^{2})^5=x^{2(5)}=x^{10}$

$(x^{4})^3=x^{4(3)}=x^{12}$

$(x^{3}y^{2} )^2=x^{3(2)}y^{2(2)}=x^6y^4$

When an exponent is negative, you move it to the other side of the fraction to make the exponent positive.

For example:

$x^{-2}$ or $\frac{x^{-2}}{1} =\frac{1}{x^2}$

$\frac{1}{y^{-3}} =\frac{y^3}{1}$ or y³

$(p^{10} r^{-5})^{\frac{1}{5}}=p^{10(\frac{1}{5})}r^{-5(\frac{1}{5})}=p^{\frac{10}{5}} r^{\frac{-5}{5}}=p^2r^{-1}=\frac{p^2}{r^1}=\frac{p^2}{r}$