Fully simplify using only positive exponents. (12x^(8)y^(3))/(18x^(6)y^(5)) Answer:

Factor out common terms: Write down the expression and factor out common terms. (12x^(8)y^(3))/(18x^(6)y^(5)) can be simplified by factoring out the common terms in the numerator and the denominator.Simplify coefficients: Simplify the coefficients (numbers) by dividing 12 by 18. 12 divided by 18 reduces to 2/3 when simplified.Simplify x terms: Simplify the x terms by subtracting the exponents. x^(8) divided by x^(6) is x^(8-6), which simplifies to x^(2).Simplify y terms: Simplify the y terms by subtracting the exponents. y^(3) divided by y^(5) is y^(3-5), which simplifies to y^(-2). Since we want only positive exponents, we can write y^(-2) as 1/y^(2).Combine simplified terms: Combine the simplified terms. The expression now is (2/3) * x^(2) * (1/y^(2)).Write final expression: Write the final simplified expression with positive exponents only. The final simplified expression is (2x^(2))/(3y^(2)).

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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{12 x^{8} y^{3}}{18 x^{6} y^{5}}

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Answer:

Factor out common terms: Write down the expression and factor out common terms. $(12x^{8}y^{3})/(18x^{6}y^{5})$ can be simplified by factoring out the common terms in the numerator and the denominator.
Simplify coefficients: Simplify the coefficients (numbers) by dividing $12$ by $18$ . $\newline$ $12$ divided by $18$ reduces to $\frac{2}{3}$ when simplified.
Simplify $x$ terms: Simplify the $x$ terms by subtracting the exponents. $\frac{x^{8}}{x^{6}}$ is $x^{(8-6)}$ , which simplifies to $x^{2}$ .
Simplify $y$ terms: Simplify the $y$ terms by subtracting the exponents. $y^{3}$ divided by $y^{5}$ is $y^{3-5}$ , which simplifies to $y^{-2}$ . Since we want only positive exponents, we can write $y^{-2}$ as $\frac{1}{y^{2}}$ .
Combine simplified terms: Combine the simplified terms. $\newline$ The expression now is $(\frac{2}{3}) \times x^{2} \times (\frac{1}{y^{2}})$ .
Write final expression: Write the final simplified expression with positive exponents only. $\newline$ The final simplified expression is $(\frac{2x^{2}}{3y^{2}})$ .