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Simplify. Express your answer using positive exponents. \newline4y3y5\frac{4y^3}{y^5}

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Multiply powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline4y3y5\frac{4y^3}{y^5}
  1. Write Expression: Write down the expression.\newlineThe expression given is 4y3y5\frac{4y^3}{y^5}.
  2. Apply Quotient Rule: Apply the quotient rule for exponents. The quotient rule states that when dividing like bases, you subtract the exponents. So, y3/y5=y(3−5)y^3/y^5 = y^{(3-5)}.
  3. Subtract Exponents: Perform the subtraction of the exponents.\newlineSubtract the exponents of yy.\newliney(3−5)=y−2y^{(3-5)} = y^{-2}.
  4. Express Negative Exponent: Express the negative exponent as a positive exponent.\newlineA negative exponent means that the base is on the wrong side of the fraction line, so we flip it to the other side to make the exponent positive.\newliney−2=1y2y^{-2} = \frac{1}{y^2}.
  5. Combine Coefficient: Combine the coefficient with the simplified exponent expression.\newlineThe coefficient 44 remains unchanged, and we multiply it by the result from Step 44.\newline4×(1y2)=4y2.4 \times \left(\frac{1}{y^2}\right) = \frac{4}{y^2}.

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