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Popular >

simplify sqrt((-2x)^6)

Solution

simplify

(- 2 x)^{6}

Solution

- 8 x^{3}

Solution steps

(- 2 x)^{6}

Apply radical rule:

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

6 \cdot \frac{1}{2} = 3

= (- 2 x)^{3}

Apply exponent rule:

(- a)^{n} = - a^{n},

if

n

is odd

(- 2 x)^{3} = - (2 x)^{3}

= - (2 x)^{3}

Apply exponent rule:

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

(2 x)^{3} = 2^{3} x^{3}

= - 2^{3} x^{3}

2^{3} = 8

= - 8 x^{3}

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Frequently Asked Questions (FAQ)

What is sqrt((-2x)^6) ?
The solution to sqrt((-2x)^6) is -8x^3