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Simplify. Express your answer using a single exponent.\newline(11b9)2(11b^9)^2

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Q. Simplify. Express your answer using a single exponent.\newline(11b9)2(11b^9)^2
  1. Apply Power Rule: Apply the power of a power rule.\newlineThe power of a power rule states that when you raise a power to another power, you multiply the exponents. In this case, we have (11b9)2(11b^9)^2, so we will apply the rule to both the base 1111 and the exponent of bb.\newline(11b9)2=112×(b9)2(11b^9)^2 = 11^2 \times (b^9)^2
  2. Calculate 11211^2: Calculate 11211^2.\newline11211^2 is 1111 multiplied by itself.\newline112=11×11=12111^2 = 11 \times 11 = 121
  3. Calculate (b9)2(b^9)^2: Calculate (b9)2(b^9)^2. Using the power of a power rule, we multiply the exponents 99 and 22. (b9)2=b(9×2)=b18(b^9)^2 = b^{(9 \times 2)} = b^{18}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have 121121 from Step 22 and b18b^{18} from Step 33. We multiply these together to get the final simplified expression.\newline121×b18=121b18121 \times b^{18} = 121b^{18}