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Simplify. Express your answer using a single exponent.\newline(7d2)2(7d^2)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(7d2)2(7d^2)^2
  1. Apply Power Rule: Apply the power of a power rule to (7d2)2(7d^2)^2. The power of a power rule states that (am)n=am∗n(a^m)^n = a^{m*n}. We will apply this rule to both the numerical coefficient and the variable with its exponent. (7d2)2=72×(d2)2(7d^2)^2 = 7^2 \times (d^2)^2
  2. Calculate Square of 77: Calculate the square of 77. 72=7×7=497^2 = 7 \times 7 = 49
  3. Apply Power Rule to d2d^2: Apply the power of a power rule to (d2)2(d^2)^2.(d2)2=d(2∗2)=d4(d^2)^2 = d^{(2*2)} = d^4
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineThe simplified expression is 49×d449 \times d^4.

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