#(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." #

# \ #

# "Summarizing:" #

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