$$ k \quad ( x y ^ { 3 } ) ^ { \frac { 1 } { 2 } } imes \frac { x ^ { \frac { 1 } { 2 } } y ^ { \frac { 1 } { 2 } } } { x y ^ { 4 } } $$

Question

$$ k \quad ( x y ^ { 3 } ) ^ { \frac { 1 } { 2 } } 	imes \frac { x ^ { \frac { 1 } { 2 } } y ^ { \frac { 1 } { 2 } } } { x y ^ { 4 } } $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ k*(x*y^3)^(1/2)*((x^(1/2)*y^(1/2))/(x*y^4)) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$k\left(xy^{3}ight)^{\frac{1}{2}}\left(\frac{\left(x^{\frac{1}{2}}y^{\frac{1}{2}}ight)}{\left(xy^{4}ight)}ight)$$
- step1: Evaluate:
  $$k\left(xy^{3}ight)^{\frac{1}{2}}	imes \frac{x^{\frac{1}{2}}y^{\frac{1}{2}}}{xy^{4}}$$
- step2: Multiply the terms:
  $$kx^{\frac{1}{2}}y^{\frac{3}{2}}	imes \frac{x^{\frac{1}{2}}y^{\frac{1}{2}}}{xy^{4}}$$
- step3: Multiply the terms:
  $$\frac{kx^{\frac{1}{2}}y^{\frac{3}{2}}x^{\frac{1}{2}}y^{\frac{1}{2}}}{xy^{4}}$$
- step4: Multiply the terms:
  $$\frac{kxy^{2}}{xy^{4}}$$
- step5: Reduce the fraction:
  $$\frac{k}{y^{2}}$$
The simplified expression is $$ \frac{k}{y^{2}} $$.
The simplified expression is $$ \frac{k}{y^{2}} $$.

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