What is \sqrt[4]{\sqrt[3]{7y^6z^3}} ?

The solution to \sqrt[4]{\sqrt[3]{7y^6z^3}} is \sqrt[12]{7}\sqrt[12]{y^6z^3}

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simplify \sqrt[4]{\sqrt[3]{7y^6z^3}}

simplify

Solution steps

Apply radical rule:

= ((7 y^{6} z^{3})^{\frac{1}{3}})^{\frac{1}{4}}

Apply exponent rule:

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

assuming

a \geq 0

= (7 y^{6} z^{3})^{\frac{1}{3} \cdot \frac{1}{4}}

\frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}

= (7 y^{6} z^{3})^{\frac{1}{12}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

1.26 \cdot 1 0^{- 4}

1.26 \cdot 1 0^{- 2}

2

(3.87 \times 1 0^{- 5}) (5.96 \times 1 0^{- 9})

(a^{2} b c^{2}) (b^{2} c^{3}) (9 a)

What is \sqrt[4]{\sqrt[3]{7y^6z^3}} ?
The solution to \sqrt[4]{\sqrt[3]{7y^6z^3}} is \sqrt[12]{7}\sqrt[12]{y^6z^3}