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

The solution to (-5a^{3/2})(2a^{1/2}) is -10a^2

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

simplify

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

- 10 a^{2}

Solution steps

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

Apply rule:

(- a) = - a

(- 5 a^{\frac{3}{2}}) = - 5 a^{\frac{3}{2}}

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

Multiply the numbers:

- 5 \cdot 2 = - 10

= - 10 a^{\frac{3}{2}} a^{\frac{1}{2}}

Apply exponent rule:

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

a^{\frac{3}{2}} a^{\frac{1}{2}} = a^{\frac{3}{2} + \frac{1}{2}}

= - 10 a^{\frac{3}{2} + \frac{1}{2}}

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

= - 10 a^{2}

lo g_{10} (0.0000001)

\frac{98}{2} (2000 + 1000 (98 - 1))

2 \cdot 24

(\frac{2}{9 2})^{2} + (\frac{5}{9 2})^{2}

\frac{5}{2} - \frac{7}{2}