What is 10^{1/4}*40^{1/4}*5^{1/2} ?

The solution to 10^{1/4}*40^{1/4}*5^{1/2} is 10

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simplify 10^{1/4}40^{1/4}5^{1/2}

simplify

1 0^{\frac{1}{4}} \cdot 4 0^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

10

Solution steps

1 0^{\frac{1}{4}} \cdot 4 0^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Apply exponent rule:

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

1 0^{\frac{1}{4}} \cdot 4 0^{\frac{1}{4}} = (10 \cdot 40)^{\frac{1}{4}}

= 5^{\frac{1}{2}} (10 \cdot 40)^{\frac{1}{4}}

Multiply the numbers:

10 \cdot 40 = 400

= 40 0^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Factor integer

400 = 5^{2} \cdot 16

= (5^{2} \cdot 16)^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(5^{2} \cdot 16)^{\frac{1}{4}} = (5^{2})^{\frac{1}{4}} \cdot 1 6^{\frac{1}{4}}

= (5^{2})^{\frac{1}{4}} \cdot 1 6^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(5^{2})^{\frac{1}{4}} = 5^{2 \cdot \frac{1}{4}}

= 5^{2 \cdot \frac{1}{4}} \cdot 1 6^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Refine

= 5^{\frac{1}{2}} \cdot 1 6^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Apply exponent rule:

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

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

= 1 6^{\frac{1}{4}} \cdot 5^{\frac{1}{2} + \frac{1}{2}}

1 6^{\frac{1}{4}} = 2

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

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

= 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10

0.027 \cdot 3^{- 2}

(\frac{\frac{3}{125}}{2} - \frac{\frac{1}{25}}{2}) \cdot e^{- \frac{27}{1000} \cdot \frac{1}{3}}

3 x^{5} e^{- y}

0.05 \cdot 1 0^{- 2}

0.3 \cdot 1 0^{- 5}

What is 10^{1/4}*40^{1/4}*5^{1/2} ?
The solution to 10^{1/4}*40^{1/4}*5^{1/2} is 10