What is \sqrt[6]{sqrt(64x^6)} ?

The solution to \sqrt[6]{sqrt(64x^6)} is sqrt(2)sqrt(x)

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simplify \sqrt[6]{sqrt(64x^6)}

simplify

2 x

Solution steps

Apply radical rule:

= ((64 x^{6})^{\frac{1}{2}})^{\frac{1}{6}}

Apply exponent rule:

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

assuming

a \geq 0

= (64 x^{6})^{\frac{1}{2} \cdot \frac{1}{6}}

\frac{1}{2} \cdot \frac{1}{6} = \frac{1}{12}

= (64 x^{6})^{\frac{1}{12}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply exponent rule:

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

x^{6} = x^{0.5 \cdot 12} = (x)^{12}

Apply radical rule:

assuming

a \geq 0

= 2 x

(a^{3} x^{6}) (a^{4} x^{2})

2^{2 \circ} 2^{4}

n C r (6, 3) (0.5)^{3} (0.5)^{6 - 3}

(x 2) (y 2)

What is \sqrt[6]{sqrt(64x^6)} ?
The solution to \sqrt[6]{sqrt(64x^6)} is sqrt(2)sqrt(x)