What is 2^{1/2}(2^{1/2}*3^{3/4}) ?

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

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simplify 2^{1/2}(2^{1/2}*3^{3/4})

simplify

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

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

Decimal

4.55901 \dots

Solution steps

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

Apply exponent rule:

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

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

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

Combine the fractions

\frac{1}{2} + \frac{1}{2} : 1

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

Apply rule

a^{1} = a

2^{1} = 2

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

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7.1 \cdot 1 0^{- 15} \cdot 0.13 3^{7} \cdot 9 0^{\frac{4}{3}}

(8 x)^{2}

4 a

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