Question

I need help on doing (2a^-6 b^4)^3 • 2a^-3 b^-5?

Answer 1

Steps

So here are a few rules with exponents that we will be applying for this problem:

• Powering a power: $(x^m)^n=x^{m*n}$
• Multiplying powers with the same base: $x^m*x^n=x^{m+n}$
• Converting negative exponents to positive exponents: $x^{-m}=\frac{1}{m^n}\ \textsf{//}\ \frac{1}{x^{-m}}=x^m$

Firstly, solve the outermost power:

$(2a^{-6} b^4)^3*2a^{-3} b^{-5}\\2^3a^{-6*3} b^{4*3}*2a^{-3} b^{-5}\\8a^{-18}b^{12}*2a^{-3}b^{-5}$

Next, multiply:

$8a^{-18}b^{12}*2a^{-3}b^{-5}\\8*2a^{-18+(-3)}b^{12+(-5)}\\16a^{-21}b^7$

Finally, convert the negative exponents:

$16a^{-21}b^7\\\\\frac{16b^7}{a^{21}}$

Answer

In short, your final answer is $\frac{16b^7}{a^{21}}$