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Simplify. Express your answer using a single exponent.\newline(9r9)2(9r^9)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(9r9)2(9r^9)^2
  1. Apply power rule: Apply the power of a power rule to the expression (9r9)2(9r^9)^2. The power of a power rule states that (am)n=am∗n(a^m)^n = a^{m*n}. Therefore, we need to apply this rule to both the numerical part and the variable part of the expression. (9r9)2=92×(r9)2(9r^9)^2 = 9^2 \times (r^9)^2
  2. Calculate 929^2: Calculate 929^2. \newline92=9×9=819^2 = 9 \times 9 = 81
  3. Apply power rule to (r9)2(r^9)^2: Apply the power of a power rule to (r9)2(r^9)^2.(r9)2=r(9∗2)=r18(r^9)^2 = r^{(9*2)} = r^{18}
  4. Combine results: Combine the results from Step 22 and Step 33.\newlineThe simplified expression is 81×r18.81 \times r^{18}.

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