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Fully simplify using only positive exponents.

(15x^(4)y^(2))/(3xy^(4))
Answer:

Fully simplify using only positive exponents.\newline15x4y23xy4 \frac{15 x^{4} y^{2}}{3 x y^{4}} \newlineAnswer:

Full solution

Q. Fully simplify using only positive exponents.\newline15x4y23xy4 \frac{15 x^{4} y^{2}}{3 x y^{4}} \newlineAnswer:
  1. Divide Coefficients: Divide the coefficients.\newlineDivide the numerical coefficients 1515 by 33.\newline15÷3=515 \div 3 = 5
  2. Simplify xx Terms: Simplify the xx terms.\newlineDivide x4x^{4} by xx to simplify the xx terms using the property xa/xb=x(ab)x^{a}/x^{b} = x^{(a-b)}.\newlinex4÷x=x(41)=x3x^{4} \div x = x^{(4-1)} = x^{3}
  3. Simplify yy Terms: Simplify the yy terms.\newlineDivide y2y^{2} by y4y^{4} to simplify the yy terms using the property ya/yb=yaby^{a}/y^{b} = y^{a-b}.\newliney2÷y4=y24=y2y^{2} \div y^{4} = y^{2-4} = y^{-2}\newlineSince we want only positive exponents, we can write y2y^{-2} as 1/y21/y^{2}.
  4. Combine Results: Combine the results.\newlineCombine the results from steps 11, 22, and 33 to get the final simplified expression.\newline5×x3×(1y2)5 \times x^{3} \times \left(\frac{1}{y^{2}}\right)

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