What is (sqrt(16^3))^{1/4} ?

The solution to (sqrt(16^3))^{1/4} is 2*2^{1/2}

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simplify (sqrt(16^3))^{1/4}

simplify

(1 6^{3})^{\frac{1}{4}}

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

Solution steps

(1 6^{3})^{\frac{1}{4}}

1 6^{3} = 64

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

Prime factorization of

64 : 2^{6}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

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

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

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

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

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

e^{- 0.4}

- 3^{2}

e^{x} \times e^{- x}

5.18 \cdot 1 0^{- 3} \cdot 410

3^{\frac{2}{3}} y 6^{\frac{2}{3}}