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5^(2)*5^(6)

52∗565^{2} * 5^{6}

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Full solution

Q. 52∗565^{2} * 5^{6}
  1. Recognize base and exponents: Step 11: Recognize the base and exponents.\newlineWe have two terms with the same base 55 raised to different exponents 22 and 66. We need to multiply these terms.\newlineCalculation: 52×565^{2} \times 5^{6}
  2. Apply exponent multiplication rule: Step 22: Apply the exponent multiplication rule.\newlineWhen multiplying powers with the same base, add the exponents.\newlineCalculation: 5(2+6)=585^{(2+6)} = 5^{8}
  3. Calculate final value: Step 33: Calculate the final value.\newlineSimplify 585^{8} by multiplying 55 by itself 88 times.\newlineCalculation: 5×5×5×5×5×5×5×5=3906255 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 390625

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