Question

Simplify the expression as much as possible and make all exponents positive. (2a^-3b5)^4(8a^-5b^-6)^-2

Answer 1

\(\Large \left( 2a^{-3}b^5 \right)^4\left( 8a^{-5}b^{-6} \right)^{-2} ?\)

Answer 2

Yes

Answer 3

I have no idea how to go about this...

Answer 4

@jdoe0001

Answer 5

\(\bf \left( 2a^{-3}b^5 \right)^{\color{blue}{ 4}}\left( 8a^{-5}b^{-6} \right)^{{\color{brown}{ -2}}}
\\ \quad \\

2^{\color{blue}{ 4}}a^{-3\cdot {\color{blue}{ 4}}}b^{5\cdot {\color{blue}{ 4}}}8^{\color{brown}{ -2}}a^{-5\cdot {\color{brown}{ -2}}}b^{-6\cdot {\color{brown}{ -2}}}
\\ \quad \\
2^4a^{-12}b^{20}8^{-2}a^{10}b^{12}
\\ \quad \\
2^4\cdot 8^{-2}\cdot a^{-12}\cdot a^{10}\cdot b^{20}\cdot b^{12}
\\ \quad \\
2^4\cdot {\color{brown}{ \cfrac{1}{8^2} }}\cdot a^{-12}\cdot a^{10}\cdot b^{20}\cdot b^{12}\)

and use the exponent rules, to combine the terms with the same base
that is, "a" and "b"