What is (3x^{1/2})(-2x^{5/2}) ?

The solution to (3x^{1/2})(-2x^{5/2}) is -6x^3

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simplify (3x^{1/2})(-2x^{5/2})

simplify

(3 x^{\frac{1}{2}}) (- 2 x^{\frac{5}{2}})

- 6 x^{3}

Solution steps

(3 x^{\frac{1}{2}}) (- 2 x^{\frac{5}{2}})

Apply rule:

a (- b) = - ab

(3 x^{\frac{1}{2}}) (- 2 x^{\frac{5}{2}}) = - 3 x^{\frac{1}{2}} \cdot 2 x^{\frac{5}{2}}

= - 3 x^{\frac{1}{2}} \cdot 2 x^{\frac{5}{2}}

Multiply the numbers:

- 3 \cdot 2 = - 6

= - 6 x^{\frac{1}{2}} x^{\frac{5}{2}}

Apply exponent rule:

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

x^{\frac{1}{2}} x^{\frac{5}{2}} = x^{\frac{1}{2} + \frac{5}{2}}

= - 6 x^{\frac{1}{2} + \frac{5}{2}}

\frac{1}{2} + \frac{5}{2} = 3

= - 6 x^{3}

50 \cdot 9

\frac{81}{45}

43 + 62 - 23

- \frac{x}{2} + x

17 (\frac{1}{17} + \frac{4}{17})