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Simplify. Express your answer using a single exponent.\newline(7y2)2(7y^2)^2

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Q. Simplify. Express your answer using a single exponent.\newline(7y2)2(7y^2)^2
  1. Apply power rule: Apply the power of a power rule.\newlineThe power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have (7y2)2(7y^2)^2, which means we need to apply the exponent of 22 to both 77 and y2y^2.\newline(7y2)2=72×(y2)2(7y^2)^2 = 7^2 \times (y^2)^2
  2. Calculate 727^2: Calculate 727^2. 727^2 means 77 multiplied by itself, which is 4949. 72=497^2 = 49
  3. Calculate (y2)2(y^2)^2: Calculate (y2)2(y^2)^2. Using the power of a power rule, we multiply the exponents. Since the base is yy and the exponents are both 22, we get yy to the power of 2×22 \times 2, which is y4y^4. (y2)2=y(22)=y4(y^2)^2 = y^{(2*2)} = y^4
  4. Combine results: Combine the results.\newlineNow we combine the results from Step 22 and Step 33 to get the final simplified expression.\newline(7y2)2=49×y4(7y^2)^2 = 49 \times y^4