What is 6^{1/2}*2^{1/4}*1^{1/4} ?

The solution to 6^{1/2}*2^{1/4}*1^{1/4} is 3^{1/2}*2^{3/4}

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simplify 6^{1/2}2^{1/4}1^{1/4}

simplify

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

3^{\frac{1}{2}} \cdot 2^{\frac{3}{4}}

Decimal Notation

2.91295 \dots

Solution steps

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

Apply exponent rule:

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

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

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

Multiply the numbers:

2 \cdot 1 = 2

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

Factor integer

6 = 2 \cdot 3

= (2 \cdot 3)^{\frac{1}{2}} \cdot 2^{\frac{1}{4}}

Apply exponent rule:

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

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

= 2^{\frac{1}{2}} \cdot 3^{\frac{1}{2}} \cdot 2^{\frac{1}{4}}

Apply exponent rule:

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

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

= 3^{\frac{1}{2}} \cdot 2^{\frac{1}{2} + \frac{1}{4}}

2^{\frac{1}{2} + \frac{1}{4}} = 2^{\frac{3}{4}}

= 3^{\frac{1}{2}} \cdot 2^{\frac{3}{4}}

2 π e^{2 π t} \cdot 2 e^{π t}

m^{x} n^{x} y^{x}

\frac{a ^{2}}{( s + a ) ^{2}}

2 π \cdot 1 0^{6} \cdot (- 10) \cdot 1 0^{- 9}

1 \cdot (1.435 \cdot (\frac{1}{2})^{- 0.921})

What is 6^{1/2}*2^{1/4}*1^{1/4} ?
The solution to 6^{1/2}*2^{1/4}*1^{1/4} is 3^{1/2}*2^{3/4}