What is \sqrt[2 1/2 ]{16^{1 1/4}} ?

The solution to \sqrt[2 1/2 ]{16^{1 1/4}} is 4

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simplify \sqrt[2 1/2 ]{16^{1 1/4}}

simplify

4

Solution steps

Convert mixed numbers to improper fractions:

1 \frac{1}{4} = \frac{5}{4}

Convert mixed numbers to improper fractions:

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

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

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

= 16

Factor the number:

16 = 4^{2}

= 4^{2}

Apply radical rule:

4^{2} = 4

= 4

7.6 \cdot 1 0^{- 2}

7.6 \cdot 1 0^{- 3}

1 0^{- 2} \cdot 63.4

e^{- \frac{1}{2} l n (16)}

What is \sqrt[2 1/2 ]{16^{1 1/4}} ?
The solution to \sqrt[2 1/2 ]{16^{1 1/4}} is 4