Q. Simplify. Express your answer using positive exponents.(10g2)(10g6)
Identify Components: Identify the components of the expression that can be combined.We have two terms, 10g2 and 10g6, which can be multiplied together. We will group the coefficients (the numbers) and the variables with their exponents separately.
Multiply Coefficients: Multiply the coefficients.The coefficients are 10 and 10. Multiplying them together gives us:10×10=100
Apply Product Rule: Apply the product rule for exponents.When multiplying powers with the same base, we add the exponents. The base here is g, with exponents 2 and 6.g2×g6=g(2+6)=g8
Combine Results: Combine the results from Step 2 and Step 3.We have found that 10×10=100 and g2×g6=g8. Now we combine these results to express the simplified form of the original expression:(10g2)(10g6)=100g8
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