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Popular >

simplify (sqrt(-72))^3

Solution

simplify

(- 72)^{3}

Solution

- 4322 i

Solution steps

(- 72)^{3}

- 72 = 62 i

= (62 i)^{3}

Apply exponent rule:

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

(62 i)^{3} = 6^{3} (2)^{3} i^{3}

= 6^{3} (2)^{3} i^{3}

6^{3} = 216

= 216 (2)^{3} i^{3}

(2)^{3} = 22

= 216 \cdot 22 i^{3}

Multiply the numbers:

216 \cdot 2 = 432

= 4322 i^{3}

Simplify

i^{3} : - i

= 4322 (- i)

Apply rule:

a (- b) = - ab

4322 (- i) = - 4322 i

= - 4322 i

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Frequently Asked Questions (FAQ)

What is (sqrt(-72))^3 ?
The solution to (sqrt(-72))^3 is -432sqrt(2)i