(y^5x^3)/(y^5x^4) simplify?

1 Answer
Feb 14, 2018

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\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ { y^5 x^3 } / { y^5 x^4 } \ = \ x^{ -1 } \quad.

Explanation:

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"One way to do this is as below. The main tool used here is the"
"Subtraction Rule for Exponents."

"Here we go:"

{ y^5 x^3 } / { y^5 x^3 } \ = \ y^5/y^5 \cdot x^3 / x^4 \ = \ y^{ 5 - 5 } \cdot x^{ 3 - 4 } \qquad \qquad \qquad \qquad \quad "Subtraction Rule"

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = \ y^{ 0 } \cdot x^{ -1 }

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = \1 \cdot x^{ -1 } \qquad \qquad \qquad \quad "Zero Exponent Definition"

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = x^{ -1 }

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = 1 / x \quad. \qquad \quad \quad \ "Negative Exponent Definition"

"This is our answer."

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"Summarizing:"

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ { y^5 x^3 } / { y^5 x^4 } \ = \ x^{ -1 } \quad.