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Fully simplify using only positive exponents. (5x^(4)y^(2))/(125x^(3)y^(4)) Answer:

Fully simplify using only positive exponents.\newline5x4y2125x3y4 \frac{5 x^{4} y^{2}}{125 x^{3} y^{4}} \newlineAnswer:

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Full solution

Q. Fully simplify using only positive exponents.\newline5x4y2125x3y4 \frac{5 x^{4} y^{2}}{125 x^{3} y^{4}} \newlineAnswer:
  1. Simplify coefficients: Simplify the coefficients.\newlineThe coefficient 55 can be divided by 125125 to simplify the fraction.\newline(5125)=125(\frac{5}{125}) = \frac{1}{25}
  2. Simplify xx terms: Simplify the xx terms using the quotient rule for exponents.\newlineThe quotient rule states that am/an=a(m−n)a^{m}/a^{n} = a^{(m-n)} when aa is not equal to 00.\newlinex4/x3=x(4−3)=x1=xx^{4}/x^{3} = x^{(4-3)} = x^{1} = x
  3. Simplify yy terms: Simplify the yy terms using the quotient rule for exponents.y2y4=y(2−4)=y−2\frac{y^{2}}{y^{4}} = y^{(2-4)} = y^{-2}
  4. Rewrite with positive exponents: Rewrite the expression with only positive exponents.\newlineSince we cannot have negative exponents in the final answer, we move y−2y^{-2} to the denominator to make the exponent positive.\newline(125)x(y−2)=(125)x/(y2)(\frac{1}{25})x(y^{-2}) = (\frac{1}{25})x/(y^{2})
  5. Combine simplified parts: Combine all the simplified parts to write the final answer. (125)x/(y2)(\frac{1}{25})x/(y^{2})

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