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Fully simplify using only positive exponents.

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

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

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Simplify radical expressions with root inside the root

Full solution

Q. Fully simplify using only positive exponents.

\newline

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

\newline

Answer:

Identify Base Numbers: Identify the base numbers and their exponents in the numerator and the denominator. $\newline$ We have $125x^{3}y^{2}$ in the numerator and $x^{5}y^{3}$ in the denominator.
Simplify Numerical Part: Simplify the numerical part of the expression. $125$ is a perfect cube, as $125 = 5^3$ . So, we can write $125$ as $5^3$ .
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ The quotient rule states that $a^{m}/a^{n} = a^{m-n}$ when $m > n$ . $\newline$ For $x^{3}/x^{5}$ , we subtract the exponents: $3 - 5 = -2$ . $\newline$ For $y^{2}/y^{3}$ , we subtract the exponents: $2 - 3 = -1$ .
Write Expression with Exponents: Write the expression with the simplified exponents. $\newline$ We have $(5^3 \times x^{-2} \times y^{-1})$ .
Move Terms to Denominator: Since we want only positive exponents, we move the terms with negative exponents to the denominator. $\newline$ This gives us $5^3 / (x^2 \cdot y)$ .
Calculate Value of $5^3$ : Calculate the value of $5^3$ . $\newline$ $5^3 = 5 \times 5 \times 5 = 125$ .
Write Final Expression: Write the final simplified expression. $\newline$ The final expression is $\frac{125}{x^2 \cdot y}$ .

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