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Divide. $\newline$ $(25 xz^{0}+20x^{6}z^{0})\div(-4x^{3}z^{5})$ $\newline$ Simplify your answer as much as possible.

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Multiply and divide rational expressions

Full solution

Q. Divide.

\newline

(25 xz^{0}+20x^{6}z^{0})\div(-4x^{3}z^{5})

\newline

Simplify your answer as much as possible.

Simplify terms with exponents: First, simplify the terms with exponents raised to the power of $0$ , since anything raised to the power of $0$ is $1$ . So, $xz^{0}$ becomes $x\cdot 1 = x$ and $x^{6}z^{0}$ becomes $x^{6}\cdot 1 = x^{6}$ .
Rewrite expression: Now, rewrite the expression with the simplified terms: $\frac{25x + 20x^{6}}{-4x^{3}z^{5}}$ .
Split into fractions: Next, split the division into two separate fractions: $\frac{25x}{-4x^{3}z^{5}}$ + $\frac{20x^{6}}{-4x^{3}z^{5}}$ .
Simplify each fraction: Simplify each fraction by dividing the coefficients and subtracting the exponents of like bases: $\frac{25}{-4} \times \frac{x}{x^{3}} \times \frac{1}{z^{5}} + \frac{20}{-4} \times \frac{x^{6}}{x^{3}} \times \frac{1}{z^{5}}$ .
Perform division and subtraction: Perform the division and subtraction of exponents: $(-\frac{25}{4}) \cdot (x^{1-3}) \cdot (z^{0-5}) + (-\frac{20}{4}) \cdot (x^{6-3}) \cdot (z^{0-5})$ .
Simplify exponents and coefficients: Simplify the exponents and coefficients: $(-\frac{25}{4}) \times (x^{-2}) \times (z^{-5}) + (-5) \times (x^{3}) \times (z^{-5})$ .
Rewrite with negative exponents: Since $x^{-2}$ means $1/x^{2}$ and $z^{-5}$ means $1/z^{5}$ , rewrite the expression: $\newline$ $(-\frac{25}{4}x^{2}z^{5}) + (-\frac{5x^{3}}{z^{5}})$ .
Combine terms over common denominator: Combine the terms over a common denominator, which is $4x^{2}z^{5}$ : $\newline$ $(-25 - 20x^{3} \times 4) / (4x^{2}z^{5})$ .

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