What is \sqrt[4]{\sqrt[5]{625}} ?

The solution to \sqrt[4]{\sqrt[5]{625}} is \sqrt[5]{5}

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simplify \sqrt[4]{\sqrt[5]{625}}

simplify

Decimal Notation

1.37972 \dots

Solution steps

Apply radical rule:

= (62 5^{\frac{1}{5}})^{\frac{1}{4}}

Apply exponent rule:

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

= 62 5^{\frac{1}{5} \cdot \frac{1}{4}}

\frac{1}{5} \cdot \frac{1}{4} = \frac{1}{20}

= 62 5^{\frac{1}{20}}

Factor the number:

625 = 5^{4}

Apply exponent rule:

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

(4 - x)^{- 1}

8.85 \cdot 1 0^{- 12} \cdot \frac{42 \cdot 1 0 ^{- 4}}{1.3 \cdot 1 0 ^{- 3}}

2 a + 3 b \cdot 3 a - 4 b

What is \sqrt[4]{\sqrt[5]{625}} ?
The solution to \sqrt[4]{\sqrt[5]{625}} is \sqrt[5]{5}