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Simplify. Express your answer using a single exponent.\newline(11v3)2(11v^3)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(11v3)2(11v^3)^2
  1. Apply Power Rule: Apply the power of a power rule to (11v3)2(11v^3)^2. The power of a power rule states that (am)n=am∗n(a^m)^n = a^{m*n}. Therefore, we need to apply the exponent of 22 to both the base 1111 and the exponent of v3v^3. (11v3)2=112∗(v3)2(11v^3)^2 = 11^2 * (v^3)^2
  2. Calculate 11211^2: Calculate 11211^2.\newline11211^2 means 1111 multiplied by itself.\newline112=11×11=12111^2 = 11 \times 11 = 121
  3. Calculate (v3)2(v^3)^2: Calculate (v3)2(v^3)^2. Using the power of a power rule, we multiply the exponents. (v3)2=v(3∗2)=v6(v^3)^2 = v^{(3*2)} = v^6
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have 121121 from 11211^2 and v6v^6 from (v3)2(v^3)^2. Multiplying these together gives us the final simplified expression.\newline121×v6=121v6121 \times v^6 = 121v^6

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