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

Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression. Divide 30 by 6 to simplify the coefficient. 30 / 6 = 5Simplify x Terms: Simplify the x terms using the laws of exponents. Subtract the exponent of x in the denominator from the exponent of x in the numerator. x^(2) / x^(6) = x^(2-6) = x^(-4) Since we want only positive exponents, x^(-4) can be written as 1/x^(4).Simplify y Terms: Simplify the y terms using the laws of exponents. Subtract the exponent of y in the denominator from the exponent of y in the numerator. y / y^(6) = y^(1-6) = y^(-5) Since we want only positive exponents, y^(-5) can be written as 1/y^(5).Combine Coefficients and Variables: Combine the simplified coefficients and variables. Combine the results from steps 1, 2, and 3. 5 * (1/x^(4)) * (1/y^(5)) = 5 / (x^(4)y^(5))

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Q. Fully simplify using only positive exponents.

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\frac{30 x^{2} y}{6 x^{6} y^{6}}

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Answer:

Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression. $\newline$ Divide $30$ by $6$ to simplify the coefficient. $\newline$ $\frac{30}{6} = 5$
Simplify $x$ Terms: Simplify the $x$ terms using the laws of exponents. $\newline$ Subtract the exponent of $x$ in the denominator from the exponent of $x$ in the numerator. $\newline$ $\frac{x^{2}}{x^{6}} = x^{2-6} = x^{-4}$ $\newline$ Since we want only positive exponents, $x^{-4}$ can be written as $\frac{1}{x^{4}}$ .
Simplify $y$ Terms: Simplify the $y$ terms using the laws of exponents. $\newline$ Subtract the exponent of $y$ in the denominator from the exponent of $y$ in the numerator. $\newline$ $\frac{y}{y^{6}} = y^{1-6} = y^{-5}$ $\newline$ Since we want only positive exponents, $y^{-5}$ can be written as $\frac{1}{y^{5}}$ .
Combine Coefficients and Variables: Combine the simplified coefficients and variables. $\newline$ Combine the results from steps $1$ , $2$ , and $3$ . $\newline$ $5 \times \left(\frac{1}{x^{4}}\right) \times \left(\frac{1}{y^{5}}\right) = \frac{5}{x^{4}y^{5}}$