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Simplify. Express your answer using positive exponents.\newline(10g2)(10g6)(10g^2)(10g^6)

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Q. Simplify. Express your answer using positive exponents.\newline(10g2)(10g6)(10g^2)(10g^6)
  1. Identify Components: Identify the components of the expression that can be combined.\newlineWe have two terms, 10g210g^2 and 10g610g^6, which can be multiplied together. We will group the coefficients (the numbers) and the variables with their exponents separately.
  2. Multiply Coefficients: Multiply the coefficients.\newlineThe coefficients are 1010 and 1010. Multiplying them together gives us:\newline10×10=10010 \times 10 = 100
  3. Apply Product Rule: Apply the product rule for exponents.\newlineWhen multiplying powers with the same base, we add the exponents. The base here is gg, with exponents 22 and 66.\newlineg2×g6=g(2+6)=g8g^2 \times g^6 = g^{(2+6)} = g^8
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have found that 10×10=10010 \times 10 = 100 and g2×g6=g8g^2 \times g^6 = g^8. Now we combine these results to express the simplified form of the original expression:\newline(10g2)(10g6)=100g8(10g^2)(10g^6) = 100g^8

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