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Simplify. Express your answer using positive exponents. \newline8a7(4a6)(a5)\frac{8a^7}{(4a^6)(a^5)}

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Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline8a7(4a6)(a5)\frac{8a^7}{(4a^6)(a^5)}
  1. Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression.\newlineWe divide the coefficient in the numerator by the coefficient in the denominator.\newline84=2\frac{8}{4} = 2
  2. Apply Quotient Rule: Apply the quotient rule for exponents to simplify the variables.\newlineThe quotient rule states that when we divide powers with the same base, we subtract the exponents.\newlinea7/a6=a7−6=a1=aa^7 / a^6 = a^{7-6} = a^1 = a
  3. Multiply by a5a^5: Multiply the result from Step 22 by the remaining term a5a^5. Since we are multiplying powers with the same base, we add the exponents. a×a5=a1+5=a6a \times a^5 = a^{1+5} = a^6
  4. Combine Results: Combine the results from Step 11 and Step 33 to get the final simplified expression.\newline2×a6=2a62 \times a^6 = 2a^6

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