Fully simplify using only positive exponents. (27x^(2)y^(6))/(3x^(3)y^(7)) Answer:

Write Expression, Identify Like Terms: Write down the expression and identify like terms. (27x^(2)y^(6))/(3x^(3)y^(7)) We have powers of x and y in both the numerator and the denominator that can be simplified.Simplify Coefficients: Simplify the coefficients. Divide the coefficients 27 by 3. 27 / 3 = 9Apply Quotient Rule for Exponents (x): Apply the quotient rule for exponents to x. x^(2) / x^(3) = x^(2-3) = x^(-1) Since we want only positive exponents, we can rewrite x^(-1) as 1/x.Apply Quotient Rule for Exponents (y): Apply the quotient rule for exponents to y. y^(6) / y^(7) = y^(6-7) = y^(-1) Similarly, we can rewrite y^(-1) as 1/y.Combine Results: Combine the results from steps 2, 3, and 4. 9 * (1/x) * (1/y) = 9 / (xy)

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Algebra 2

Simplify variable expressions using properties

Full solution

Q. Fully simplify using only positive exponents.

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\frac{27 x^{2} y^{6}}{3 x^{3} y^{7}}

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Answer:

Write Expression, Identify Like Terms: Write down the expression and identify like terms. $\newline$ $\frac{27x^{2}y^{6}}{3x^{3}y^{7}}$ $\newline$ We have powers of $x$ and $y$ in both the numerator and the denominator that can be simplified.
Simplify Coefficients: Simplify the coefficients. $\newline$ Divide the coefficients $27$ by $3$ . $\newline$ $\frac{27}{3} = 9$
Apply Quotient Rule for Exponents $x$ : Apply the quotient rule for exponents to $x$ . $\frac{x^{2}}{x^{3}} = x^{2-3} = x^{-1}$ Since we want only positive exponents, we can rewrite $x^{-1}$ as $\frac{1}{x}$ .
Apply Quotient Rule for Exponents $y$ : Apply the quotient rule for exponents to $y$ . $\frac{y^{6}}{y^{7}} = y^{6-7} = y^{-1}$ Similarly, we can rewrite $y^{-1}$ as $\frac{1}{y}$ .
Combine Results: Combine the results from steps $2$ , $3$ , and $4$ . $\newline$ $9 \times \left(\frac{1}{x}\right) \times \left(\frac{1}{y}\right) = \frac{9}{xy}$