Using the basic laws of exponent

Question

I have some problems with this question. Please help me. Thanks

Simplify given expression$$ a^2 (abc)^{-2} a^3 b^7 $$

What are exponents of $a$, $b$, and $c$?

I get $3,5,-2$ as exponents of $a,b,c$ respectively. Is it correct?

Answer 1

Yes, It is correct!

$$a^2 (abc)^{-2} a^3 b^7=\frac{a^2 a^3 b^7}{(abc)^{2}}=\frac{a^3b^5}{c^2}=a^3b^5c^{-2}$$

Answer 2

Assuming that you'd like to simplify the problem then $$ a^2 (abc)^{-2} a^3 b^7= \frac{a^2 a^3 b^7}{(abc)^2}= \frac{a^{2} a^3b^7}{a^2b^2c^2}= \frac{ a^3b^7}{b^2c^2} = \frac{ a^3b^5}{c^2}=a^3b^5c^{-2} $$ Here's a MathJax Tutorial for future reference.