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

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

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

simplify

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

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

Decimal Notation

5.65685 \dots

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

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

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

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

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

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

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

Multiply the numbers:

2 \cdot 2 = 4

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

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