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Popular >

simplify sqrt(6x)^{x^2}

Solution

simplify

6 x^{x^{2}}

Solution

6^{\frac{x ^{2}}{2}} x^{\frac{x ^{2}}{2}}

Solution steps

(6 x)^{x^{2}}

Apply radical rule:

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

Simplify

\frac{1}{2} x^{2} : \frac{x ^{2}}{2}

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

Apply exponent rule:

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

= 6^{\frac{x ^{2}}{2}} x^{\frac{x ^{2}}{2}}

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Frequently Asked Questions (FAQ)

What is sqrt(6x)^{x^2} ?
The solution to sqrt(6x)^{x^2} is 6^{(x^2)/2}x^{(x^2)/2}