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Popular >

simplify 400^{1/4}

Solution

simplify

40 0^{\frac{1}{4}}

Solution

2 \cdot 5^{\frac{1}{2}}

+1

Decimal Notation

4.47213 \dots

Solution steps

40 0^{\frac{1}{4}}

Factor the number:

400 = 2 0^{2}

= (2 0^{2})^{\frac{1}{4}}

Apply exponent rule:

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

= 2 0^{2 \cdot \frac{1}{4}}

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

= 2 0^{\frac{1}{2}}

Prime factorization of

20 : 2^{2} \cdot 5

= (2^{2} \cdot 5)^{\frac{1}{2}}

Apply exponent rule:

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

(2^{2} \cdot 5)^{\frac{1}{2}} = (2^{2})^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

= (2^{2})^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

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

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

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Frequently Asked Questions (FAQ)

What is 400^{1/4} ?
The solution to 400^{1/4} is 2*5^{1/2}