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Simplify. Express your answer using positive exponents.\newline4aa8\frac{4a}{a^8}

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Q. Simplify. Express your answer using positive exponents.\newline4aa8\frac{4a}{a^8}
  1. Write Given Expression: Write down the given expression.\newlineThe given expression is 4aa8\frac{4a}{a^8}. We need to simplify this expression by dividing the terms.
  2. Apply Quotient Rule: Apply the quotient rule for exponents.\newlineThe quotient rule states that when dividing like bases, you subtract the exponents. In this case, we have a1a^1 in the numerator and a8a^8 in the denominator.\newline4aa8=4×a1−8\frac{4a}{a^8} = 4 \times a^{1-8}
  3. Subtract Exponents: Subtract the exponents.\newlineNow we subtract the exponents of aa.\newlinea(1−8)=a−7a^{(1-8)} = a^{-7}
  4. Write Positive Exponent: Write the expression with a positive exponent.\newlineSince we want to express our answer using positive exponents, we can write a−7a^{-7} as 1/a71/a^7.\newline4×a−7=4×(1/a7)4 \times a^{-7} = 4 \times (1/a^7)
  5. Simplify Expression: Simplify the expression.\newlineNow we can simplify the expression by multiplying 44 by the fraction.\newline4×(1a7)=4a74 \times \left(\frac{1}{a^7}\right) = \frac{4}{a^7}

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