What is 3sqrt(-216) ?

The solution to 3sqrt(-216) is 18sqrt(6)i

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simplify 3sqrt(-216)

simplify

3 - 216

186 i

Solution steps

3 - 216

Prime factorization of

216 : 2^{3} \cdot 3^{3}

= 3 - 2^{3} \cdot 3^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

- 2^{3} \cdot 3^{3} = - 2^{2} \cdot 2 \cdot 3^{2} \cdot 3

= 3 - 2^{2} \cdot 2 \cdot 3^{2} \cdot 3

- 2^{2} \cdot 2 \cdot 3^{2} \cdot 3 = 2^{2} 3^{2} - 2 \cdot 3

= 3 2^{2} 3^{2} - 2 \cdot 3

Apply radical rule:

a^{2} = a, a \geq 0

2^{2} = 2

= 3 \cdot 2 3^{2} - 2 \cdot 3

Apply radical rule:

a^{2} = a, a \geq 0

3^{2} = 3

= 3 \cdot 2 \cdot 3 - 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 3 \cdot 6 - 6

Multiply the numbers:

3 \cdot 6 = 18

= 18 - 6

Apply radical rule:

- a = a - 1

- 6 = 6 - 1

= 186 - 1

Apply imaginary number rule:

- 1 = i

= 186 i

(- 6 x y)^{5}

\frac{1}{4} + 4 \frac{2}{5}

5^{- 7}

\frac{x ^{- 5}}{x ^{- 2}}

y^{2} - 8 y