What is (y^2x^{1/2})(yx^{1/2}) ?

The solution to (y^2x^{1/2})(yx^{1/2}) is y^3x

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simplify (y^2x^{1/2})(yx^{1/2})

simplify

(y^{2} x^{\frac{1}{2}}) (y x^{\frac{1}{2}})

y^{3} x

Solution steps

(y^{2} x^{\frac{1}{2}}) (y x^{\frac{1}{2}})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

y^{2} y = y^{2 + 1}

= x^{\frac{1}{2}} y^{2 + 1} x^{\frac{1}{2}}

Add the numbers:

2 + 1 = 3

= x^{\frac{1}{2}} y^{3} x^{\frac{1}{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x^{\frac{1}{2}} x^{\frac{1}{2}} = x^{\frac{1}{2} + \frac{1}{2}}

= y^{3} x^{\frac{1}{2} + \frac{1}{2}}

Combine the fractions

\frac{1}{2} + \frac{1}{2} : 1

= y^{3} x^{1}

Apply rule

a^{1} = a

x^{1} = x

= y^{3} x

- 271 8^{- (- 13197)}

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\frac{3.75}{2}

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