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.)
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.