Question

1. simplify (factor if necessary).

(23)
simplify. write the answers with all variables in the numerator.

1. \\(\frac{xx^{-3}y^{5}x^{0}}{x^{2}y^{-3}xy^{2}}\\) \\((40)\\) 22. \\(\frac{kp^{2}k^{-1}p^{-3}p^{-4}}{k^{2}pp^{2}k^{-5}}\\) \\((40)\\)
2. expand by using the distributive property. write the answer with all variables in the numerator.

(46) \\(\left(\frac{x^{2}}{yp^{-4}} - \frac{x^{2}y}{p^{-4}}\
ight)\frac{x^{-2}}{y^{4}p}\\)

1. simplify by adding like terms. write the answer with all exponents negative.

(47) \\(\frac{7mx^{0}}{ym^{0}} - \frac{3m^{2}y}{my^{2}} + \frac{5m^{-3}m^{4}}{y^{-3}y^{4}} + \frac{2ymm}{my^{2}}\\)
evaluate:

Explanation:

Problem 21

Step1: Combine numerator terms

$xx^{-3}y^{5}x^{0} = x^{1-3+0}y^{5} = x^{-2}y^{5}$

Step2: Combine denominator terms

$x^{2}y^{-3}xy^{2} = x^{2+1}y^{-3+2} = x^{3}y^{-1}$

Step3: Divide and simplify exponents

$\frac{x^{-2}y^{5}}{x^{3}y^{-1}} = x^{-2-3}y^{5-(-1)} = x^{-5}y^{6}$

Step4: Move variables to numerator

$x^{-5}y^{6} = \frac{y^{6}}{x^{5}}$

Step1: Combine numerator terms

$kp^{2}k^{-1}p^{3}p^{-4} = k^{1-1}p^{2+3-4} = k^{0}p^{1} = p$

Step2: Combine denominator terms

$k^{2}pp^{2}k^{-5} = k^{2-5}p^{1+2} = k^{-3}p^{3}$

Step3: Divide and simplify exponents

$\frac{p}{k^{-3}p^{3}} = k^{3}p^{1-3} = k^{3}p^{-2}$

Step4: Move variables to numerator

$k^{3}p^{-2} = \frac{k^{3}}{p^{2}}$

Step1: Distribute the multiplier

$\frac{x^{2}}{y^{4}} \cdot \frac{x^{-2}}{p^{4}} - \frac{x^{2}y}{4} \cdot \frac{x^{-2}}{p^{4}}$

Step2: Simplify first product

$\frac{x^{2-2}}{y^{4}p^{4}} = \frac{x^{0}}{y^{4}p^{4}} = \frac{1}{y^{4}p^{4}}$

Step3: Simplify second product

$\frac{x^{2-2}y}{4p^{4}} = \frac{x^{0}y}{4p^{4}} = \frac{y}{4p^{4}}$

Step4: Combine terms

$\frac{1}{y^{4}p^{4}} - \frac{y}{4p^{4}} = \frac{4 - y^{5}}{4y^{4}p^{4}}$

Answer:

$\frac{y^{6}}{x^{5}}$

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Problem 22