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Simplify. Express your answer using a single exponent.\newline(4r2)3(4r^2)^3

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Q. Simplify. Express your answer using a single exponent.\newline(4r2)3(4r^2)^3
  1. Apply Power Rule: Apply the power to a power rule.\newlineThe power to a power rule states that when you raise a power to another power, you multiply the exponents. In this case, we have (4r2)3(4r^2)^3, which means we need to raise both 44 and r2r^2 to the power of 33.\newline(4r2)3=43×(r2)3(4r^2)^3 = 4^3 \times (r^2)^3
  2. Calculate 434^3: Calculate 434^3.\newlineTo find 434^3, we multiply 44 by itself three times.\newline43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
  3. Calculate (r2)3(r^2)^3: Calculate (r2)3(r^2)^3. To find (r2)3(r^2)^3, we multiply the exponents 22 and 33. (r2)3=r(2×3)=r6(r^2)^3 = r^{(2 \times 3)} = r^6
  4. Combine Results: Combine the results.\newlineNow we combine the results from Step 22 and Step 33 to get the final simplified expression.\newline(4r2)3=43×(r2)3=64×r6(4r^2)^3 = 4^3 \times (r^2)^3 = 64 \times r^6