What is (2/a)^{1/2}((30)/(a^5))^{1/2} ?

The solution to (2/a)^{1/2}((30)/(a^5))^{1/2} is (2*15^{1/2})/(a^3)

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simplify (2/a)^{1/2}((30)/(a^5))^{1/2}

simplify

(\frac{2}{a})^{\frac{1}{2}} (\frac{30}{a ^{5}})^{\frac{1}{2}}

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

Solution steps

(\frac{2}{a})^{\frac{1}{2}} (\frac{30}{a ^{5}})^{\frac{1}{2}}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

(\frac{2}{a})^{\frac{1}{2}} (\frac{30}{a ^{5}})^{\frac{1}{2}} = (\frac{2}{a} \cdot \frac{30}{a ^{5}})^{\frac{1}{2}}

= (\frac{2}{a} \cdot \frac{30}{a ^{5}})^{\frac{1}{2}}

Simplify

\frac{2}{a} \cdot \frac{30}{a ^{5}} : \frac{60}{a ^{6}}

= (\frac{60}{a ^{6}})^{\frac{1}{2}}

Apply radical rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}},

assuming

a \geq 0, b \geq 0

= \frac{6 0 ^{\frac{1}{2}}}{( a ^{6} ) ^{\frac{1}{2}}}

(a^{6})^{\frac{1}{2}} : a^{3}

= \frac{6 0 ^{\frac{1}{2}}}{a ^{3}}

6 0^{\frac{1}{2}} = 2 \cdot 1 5^{\frac{1}{2}}

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

(x - 1)^{2} x^{2}

x^{- 2}

(0.105) (\frac{6}{0.456})^{2}

- 2 e^{x} \cdot e^{- 2 x}

(1.4215 \cdot 1 0^{- 5}) (4.85)

What is (2/a)^{1/2}((30)/(a^5))^{1/2} ?
The solution to (2/a)^{1/2}((30)/(a^5))^{1/2} is (2*15^{1/2})/(a^3)