Fully simplify using only positive exponents. (5x^(4)y^(2))/(125x^(3)y^(4)) Answer:

Simplify coefficients: Simplify the coefficients. The coefficient 5 can be divided by 125 to simplify the fraction. (5/125) = 1/25Simplify x terms: Simplify the x terms using the quotient rule for exponents. The quotient rule states that a^(m)/a^(n) = a^(m-n) when a is not equal to 0. x^(4)/x^(3) = x^(4-3) = x^(1) = xSimplify y terms: Simplify the y terms using the quotient rule for exponents. y^(2)/y^(4) = y^(2-4) = y^(-2)Rewrite with positive exponents: Rewrite the expression with only positive exponents. Since we cannot have negative exponents in the final answer, we move y^(-2) to the denominator to make the exponent positive. (1/25)x(y^(-2)) = (1/25)x/(y^(2))Combine simplified parts: Combine all the simplified parts to write the final answer. (1/25)x/(y^(2))

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Fully simplify using only positive exponents.

(5x^(4)y^(2))/(125x^(3)y^(4))
Answer:

Fully simplify using only positive exponents. $\newline$ $\frac{5 x^{4} y^{2}}{125 x^{3} y^{4}}$ $\newline$ Answer:

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Algebra 2

Simplify radical expressions with root inside the root

Full solution

Q. Fully simplify using only positive exponents.

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\frac{5 x^{4} y^{2}}{125 x^{3} y^{4}}

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Answer:

Simplify coefficients: Simplify the coefficients. $\newline$ The coefficient $5$ can be divided by $125$ to simplify the fraction. $\newline$ $(\frac{5}{125}) = \frac{1}{25}$
Simplify $x$ terms: Simplify the $x$ terms using the quotient rule for exponents. $\newline$ The quotient rule states that $a^{m}/a^{n} = a^{(m-n)}$ when $a$ is not equal to $0$ . $\newline$ $x^{4}/x^{3} = x^{(4-3)} = x^{1} = x$
Simplify $y$ terms: Simplify the $y$ terms using the quotient rule for exponents. $\frac{y^{2}}{y^{4}} = y^{(2-4)} = y^{-2}$
Rewrite with positive exponents: Rewrite the expression with only positive exponents. $\newline$ Since we cannot have negative exponents in the final answer, we move $y^{-2}$ to the denominator to make the exponent positive. $\newline$ $(\frac{1}{25})x(y^{-2}) = (\frac{1}{25})x/(y^{2})$
Combine simplified parts: Combine all the simplified parts to write the final answer. $(\frac{1}{25})x/(y^{2})$