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Simplify. Express your answer using positive exponents.\newline5y5y3\frac{5y}{5y^3}

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Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents.\newline5y5y3\frac{5y}{5y^3}
  1. Divide and Simplify: Simplify the expression by dividing the numerator by the denominator.\newlineGiven the expression 5y5y3\frac{5y}{5y^3}, we can simplify by dividing both the coefficients (55)(\frac{5}{5}) and the variables with exponents (yy3)(\frac{y}{y^3}).\newline5y5y3=(55)×(yy3)\frac{5y}{5y^3} = (\frac{5}{5}) \times (\frac{y}{y^3})
  2. Apply Quotient Rule: Simplify the coefficients and apply the quotient rule for exponents.\newlineThe coefficients 55\frac{5}{5} simplify to 11. For the variables, we subtract the exponent in the denominator from the exponent in the numerator.\newline(55)⋅(y/y3)=1⋅y(1−3)(\frac{5}{5}) \cdot (y/y^3) = 1 \cdot y^{(1-3)}
  3. Calculate Exponent: Calculate the exponent for yy.y(1−3)=y−2y^{(1-3)} = y^{-2}However, we need to express the answer using positive exponents.
  4. Convert to Positive Exponent: Convert the negative exponent to a positive exponent.\newlineTo convert y−2y^{-2} to a positive exponent, we take the reciprocal of y2y^2.\newliney−2=1y2y^{-2} = \frac{1}{y^2}

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