Question

simplify the expression. assume no denominator is equal to 0.

\\\frac{-10x^4y^5}{2x^2y^3}\\

Explanation:

Identify the given expression

We are given the rational expression:

$$ \frac{-10x^4y^5}{2x^2y^3} $$

Our goal is to simplify this expression by dividing the coefficients and applying exponent rules to the variables.

Divide the numerical coefficients

We separate the numerical coefficients from the variable parts:

$$ \frac{-10}{2} = -5 $$

Simplify the variable x

Using the Quotient Rule of Exponents, which states that \(\frac{a^m}{a^n} = a^{m-n}\), we simplify the \(x\) terms:

$$ \frac{x^4}{x^2} = x^{4-2} = x^2 $$

Simplify the variable y

Using the same exponent rule, we simplify the \(y\) terms:

$$ \frac{y^5}{y^3} = y^{5-3} = y^2 $$

Combine the simplified parts

We multiply the simplified numerical coefficient and variable terms together:

$$ -5 \cdot x^2 \cdot y^2 = -5x^2y^2 $$

Answer:

Simplify the expression. Assume no denominator is equal to 0.

$$\frac{-10x^4y^5}{2x^2y^3} =$$

<blank>\(-5x^2y^2\)</blank>