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Simplify. Express your answer using a single exponent.\newline(11v9)2(11v^9)^2

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Powers of a power: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using a single exponent.\newline(11v9)2(11v^9)^2
  1. Apply Power Separately: Apply the power to both the base number and the variable separately.\newlineWhen raising a power to a power, we distribute the exponent to each factor within the product. \newline(11v9)2=112×(v9)2(11v^9)^2 = 11^2 \times (v^9)^2
  2. Calculate 11211^2: Calculate 11211^2.\newline112=11×11=12111^2 = 11 \times 11 = 121
  3. Calculate (v9)2(v^9)^2: Calculate (v9)2(v^9)^2.\newlineWhen raising a power to another power, we multiply the exponents.\newline(v9)2=v(9×2)=v18(v^9)^2 = v^{(9 \times 2)} = v^{18}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(11v9)2=112×(v9)2=121v18(11v^9)^2 = 11^2 \times (v^9)^2 = 121v^{18}

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