What is 3^{0.5}*(sqrt(2))^7 ?

The solution to 3^{0.5}*(sqrt(2))^7 is 8*6^{1/2}

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simplify 3^{0.5}*(sqrt(2))^7

simplify

3^{0.5} \cdot (2)^{7}

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

Decimal Notation

19.59591 \dots

Solution steps

3^{0.5} (2)^{7}

(2)^{7} : 2^{\frac{7}{2}}

= 3^{0.5} \cdot 2^{\frac{7}{2}}

2^{\frac{7}{2}} = 2^{3} \cdot 2^{\frac{1}{2}}

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

Apply exponent rule:

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

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

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

Multiply the numbers:

3 \cdot 2 = 6

= 2^{3} \cdot 6^{\frac{1}{2}}

2^{3} = 8

= 8 \cdot 6^{\frac{1}{2}}

\frac{0.000 1 ^{4}}{1. 5 ^{4}}

1.06 \cdot 10 e^{- 10}

1.13 \cdot 1 0^{- 2}

1.03 \cdot 1 0^{- 2}

1.03 \cdot 1 0^{- 4}