Steps
So here are a few rules with exponents that we will be applying for this problem:
- Powering a power: [tex](x^m)^n=x^{m*n}[/tex]
- Multiplying powers with the same base: [tex]x^m*x^n=x^{m+n}[/tex]
- Converting negative exponents to positive exponents: [tex]x^{-m}=\frac{1}{m^n}\ \textsf{//}\ \frac{1}{x^{-m}}=x^m[/tex]
Firstly, solve the outermost power:
[tex](2a^{-6} b^4)^3*2a^{-3} b^{-5}\\2^3a^{-6*3} b^{4*3}*2a^{-3} b^{-5}\\8a^{-18}b^{12}*2a^{-3}b^{-5}[/tex]
Next, multiply:
[tex]8a^{-18}b^{12}*2a^{-3}b^{-5}\\8*2a^{-18+(-3)}b^{12+(-5)}\\16a^{-21}b^7[/tex]
Finally, convert the negative exponents:
[tex]16a^{-21}b^7\\\\\frac{16b^7}{a^{21}}[/tex]
Answer
In short, your final answer is [tex]\frac{16b^7}{a^{21}}[/tex]
