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Divide. (-25 xz^(0)+20x^(6)z^(0))÷(-4x^(3)z^(5)) Simplify your answer as much as possible.

Divide.\newline(−25xz0+20x6z0)÷(−4x3z5) \left(-25 x z^{0}+20 x^{6} z^{0}\right) \div\left(-4 x^{3} z^{5}\right) \newlineSimplify your answer as much as possible.

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Multiply and divide rational expressionsright chevron icon

Full solution

Q. Divide.\newline(−25xz0+20x6z0)÷(−4x3z5) \left(-25 x z^{0}+20 x^{6} z^{0}\right) \div\left(-4 x^{3} z^{5}\right) \newlineSimplify your answer as much as possible.
  1. Simplify exponents: First, simplify the exponents where z0=1z^{0} = 1.(−25x⋅1+20x6⋅1)(−4x3z5)\frac{(-25 x \cdot 1 + 20x^{6} \cdot 1)}{(-4x^{3}z^{5})}
  2. Rewrite expression: Now, rewrite the expression without the z0z^{0} terms.−25x+20x6−4x3z5\frac{-25x + 20x^{6}}{-4x^{3}z^{5}}
  3. Divide terms: Next, divide each term in the numerator by the term in the denominator.\newline(−25x÷−4x3z5)+(20x6÷−4x3z5)(-25x \div -4x^{3}z^{5}) + (20x^{6} \div -4x^{3}z^{5})
  4. Simplify fractions: Simplify each fraction by canceling out common factors.\newline(254×1x2×1z5)+(−204×x3×1z5)(\frac{25}{4} \times \frac{1}{x^{2}} \times \frac{1}{z^{5}}) + (-\frac{20}{4} \times x^{3} \times \frac{1}{z^{5}})
  5. Reduce fractions: Reduce the fractions and simplify the xx terms.254x2z5\frac{25}{4x^{2}z^{5}} + (−5x3z5)\left(-\frac{5x^{3}}{z^{5}}\right)
  6. Combine terms: Combine the terms to get the final simplified expression. \newline(254x2z5)−(5x3z5)(\frac{25}{4}x^{2}z^{5}) - (\frac{5x^{3}}{z^{5}})

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