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simplify the expression.(-5r^2s^7)^3÷r

Sagot :

Use the laws of exponents to simplify the expression:

[tex]\frac{(-5r^2s^7)^3^{}}{r}[/tex]

We know that:

[tex]\begin{gathered} (ab)^n=a^nb^n \\ (a^n)^m=a^{n\times m} \\ \frac{a^n}{a^m}=a^{n-m} \end{gathered}[/tex]

Then:

[tex]\begin{gathered} \frac{(-5r^2s^7)^3}{r}=\frac{(-5)^3(r^2)^3(s^7)^3}{r} \\ =\frac{-125r^6s^{21}}{r} \\ =-125r^{6-1}s^{21} \\ =-125r^5s^{21} \end{gathered}[/tex]

Therefore:

[tex]\frac{(-5r^2s^7)^3}{r}=-125r^5s^{21}[/tex]

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