Fully simplify using only positive exponents. (30x^(2)y^(8))/(50x^(6)y^(7)) Answer:

Identify Coefficients and Variables: Identify the coefficients and the variables with their exponents separately to simplify the expression.Simplify Coefficients: Simplify the coefficients by dividing 30 by 50. 30 / 50 = 3 / 5Simplify x Terms: Simplify the x terms by subtracting the exponents, using the property x^a / x^b = x^(a-b). x^(2) / x^(6) = x^(2-6) = x^(-4) Since we want only positive exponents, we can write x^(-4) as 1/x^(4).Simplify y Terms: Simplify the y terms by subtracting the exponents, using the property y^a / y^b = y^(a-b). y^(8) / y^(7) = y^(8-7) = y^(1) = yCombine Coefficients and Variables: Combine the simplified coefficients and variables to get the final expression. (3/5) * (1/x^(4)) * y = (3y) / (5x^(4))

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Q. Fully simplify using only positive exponents.

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\frac{30 x^{2} y^{8}}{50 x^{6} y^{7}}

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Answer:

Identify Coefficients and Variables: Identify the coefficients and the variables with their exponents separately to simplify the expression.
Simplify Coefficients: Simplify the coefficients by dividing $30$ by $50$ . $\newline$ $\frac{30}{50} = \frac{3}{5}$
Simplify $x$ Terms: Simplify the $x$ terms by subtracting the exponents, using the property $\frac{x^a}{x^b} = x^{(a-b)}$ . $\frac{x^{2}}{x^{6}} = x^{(2-6)} = x^{-4}$ Since we want only positive exponents, we can write $x^{-4}$ as $\frac{1}{x^{4}}$ .
Simplify $y$ Terms: Simplify the $y$ terms by subtracting the exponents, using the property $\frac{y^a}{y^b} = y^{(a-b)}$ . $\frac{y^{8}}{y^{7}} = y^{(8-7)} = y^{1} = y$
Combine Coefficients and Variables: Combine the simplified coefficients and variables to get the final expression. $\newline$ $(\frac{3}{5}) \times (\frac{1}{x^{4}}) \times y = \frac{3y}{5x^{4}}$