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Simplify. Express your answer using positive exponents.\newline3y3y3\frac{3y}{3y^3}

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Multiply powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents.\newline3y3y3\frac{3y}{3y^3}
  1. Write Expression: Write down the expression to be simplified.\newlineWe have the expression 3y3y3\frac{3y}{3y^3}.
  2. Simplify Coefficients: Simplify the coefficients.\newlineBoth the numerator and the denominator have the coefficient 33, so they cancel each other out.\newline33=1\frac{3}{3} = 1
  3. Simplify Variables: Simplify the variables using the laws of exponents.\newlineWe have yy in the numerator and y3y^3 in the denominator. When dividing powers with the same base, we subtract the exponents.\newliney/y3=y1−3=y−2y/y^3 = y^{1-3} = 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 make the exponent positive.\newliney−2=1y2y^{-2} = \frac{1}{y^2}
  5. Combine Results: Combine the results from steps 22 and 44 to write the final simplified expression.\newlineSince the coefficients cancel out to 11 and we have 1y2\frac{1}{y^2} from the variables, the final simplified expression is:\newline1y2\frac{1}{y^2}

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