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Alenkinab [10]
3 years ago
14

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

Mathematics
1 answer:
aev [14]3 years ago
3 0
<h2>Steps</h2>

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}}

<h2>Answer</h2>

<u>In short, your final answer is \frac{16b^7}{a^{21}}</u>

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