Fully simplify using only positive exponents. (4x^(6)y^(6))/(8x^(3)y^(7)) Answer:

Factor out common terms: Write down the expression and factor out common terms. We have the expression (4x^(6)y^(6))/(8x^(3)y^(7)). We can simplify this by factoring out common terms in the numerator and the denominator.Divide coefficients: Divide the coefficients. Divide the numerical coefficients 4 by 8. 4/8 = 1/2Simplify x terms: Simplify the x terms. Divide the x terms using the rule x^(a)/x^(b) = x^(a-b). x^(6)/x^(3) = x^(6-3) = x^(3)Simplify y terms: Simplify the y terms. Divide the y terms using the rule y^(a)/y^(b) = y^(a-b). y^(6)/y^(7) = y^(6-7) = y^(-1) Since we want only positive exponents, we can write y^(-1) as 1/y.Combine simplified terms: Combine the simplified terms. Combine the simplified coefficients and variables. (1/2) * x^(3) * (1/y) = (x^(3))/(2y)

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Algebra 2

Simplify variable expressions using properties

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Q. Fully simplify using only positive exponents.

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\frac{4 x^{6} y^{6}}{8 x^{3} y^{7}}

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Answer:

Factor out common terms: Write down the expression and factor out common terms. $\newline$ We have the expression $(4x^{6}y^{6})/(8x^{3}y^{7})$ . We can simplify this by factoring out common terms in the numerator and the denominator.
Divide coefficients: Divide the coefficients. $\newline$ Divide the numerical coefficients $4$ by $8$ . $\newline$ $\frac{4}{8} = \frac{1}{2}$
Simplify $x$ terms: Simplify the $x$ terms. $\newline$ Divide the $x$ terms using the rule $x^{a}/x^{b} = x^{(a-b)}$ . $\newline$ $x^{6}/x^{3} = x^{(6-3)} = x^{3}$
Simplify $y$ terms: Simplify the $y$ terms. $\newline$ Divide the $y$ terms using the rule $y^{a}/y^{b} = y^{(a-b)}$ . $\newline$ $y^{6}/y^{7} = y^{(6-7)} = y^{-1}$ $\newline$ Since we want only positive exponents, we can write $y^{-1}$ as $1/y$ .
Combine simplified terms: Combine the simplified terms. $\newline$ Combine the simplified coefficients and variables. $\newline$ $(\frac{1}{2}) \times x^{3} \times (\frac{1}{y}) = \frac{x^{3}}{2y}$