Question

Simplify the following expression.
left parenthesis u Superscript 6 Baseline v Superscript negative 3 Baseline right parenthesis squared left parenthesis u cubed right parenthesis Superscript 6
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Part 1
left parenthesis u Superscript 6 Baseline v Superscript negative 3 Baseline right parenthesis squared left parenthesis u cubed right parenthesis Superscript 6equals
  
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​(Simplify your answer. Type exponential notation with positive​ exponents.)

Answer 1

To simplify the expression, we can apply the product rule of exponents:

(u^6v^-3)^2(u^3)^6

First, we square (u^6v^-3):

(u^6v^-3)^2 = u^(6*2)v^(-3*2) = u^12v^-6

Then, we raise (u^3) to the power of 6:

(u^3)^6 = u^(3*6) = u^18

Now, we can multiply the two simplified expressions:

(u^12v^-6)(u^18) = u^(12+18)v^(-6) = u^30v^-6

Therefore, the simplified expression is u^30v^-6.