Fully simplify using only positive exponents. (27x^(4)y^(2))/(9x^(4)y) Answer:

Identify Like Terms: Write down the expression and identify like terms. Expression: (27x^(4)y^(2))/(9x^(4)y) We have like terms in the numerator and denominator that can be simplified.Simplify Coefficients: Simplify the coefficients (numbers) by dividing 27 by 9. 27 divided by 9 equals 3. So, (27x^(4)y^(2))/(9x^(4)y) becomes (3x^(4)y^(2))/(x^(4)y).Cancel Common Terms: Cancel out the common x^(4) terms in the numerator and denominator. Since x^(4)/x^(4) equals 1, we can remove these terms. Now we have (3y^(2))/y.Simplify Exponents: Simplify the y terms by subtracting the exponents. According to the laws of exponents, y^(2)/y equals y^(2-1) which is y^(1) or simply y. So, (3y^(2))/y becomes 3y.

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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{27 x^{4} y^{2}}{9 x^{4} y}

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Answer:

Identify Like Terms: Write down the expression and identify like terms. $\newline$ Expression: $(27x^{4}y^{2})/(9x^{4}y)$ $\newline$ We have like terms in the numerator and denominator that can be simplified.
Simplify Coefficients: Simplify the coefficients (numbers) by dividing $27$ by $9$ . $\newline$ $27$ divided by $9$ equals $3$ . $\newline$ So, $(27x^{4}y^{2})/(9x^{4}y)$ becomes $(3x^{4}y^{2})/(x^{4}y)$ .
Cancel Common Terms: Cancel out the common $x^{4}$ terms in the numerator and denominator. $\newline$ Since $x^{4}/x^{4}$ equals $1$ , we can remove these terms. $\newline$ Now we have $(3y^{2})/y$ .
Simplify Exponents: Simplify the $y$ terms by subtracting the exponents. $\newline$ According to the laws of exponents, $y^{2}/y$ equals $y^{2-1}$ which is $y^{1}$ or simply $y$ . $\newline$ So, $(3y^{2})/y$ becomes $3y$ .