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Popular >

simplify (5i^3)^3

Solution

simplify

(5 i^{3})^{3}

Solution

125 i

Solution steps

(5 i^{3})^{3}

Apply exponent rule:

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

(5 i^{3})^{3} = 5^{3} (i^{3})^{3}

= 5^{3} (i^{3})^{3}

5^{3} = 125

= 125 (i^{3})^{3}

Apply exponent rule:

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

assuming

a \geq 0

(i^{3})^{3} = i^{3 \cdot 3}

= 125 i^{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= 125 i^{9}

Apply exponent rule:

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

i^{9} = i^{8} i

= 125 i^{8} i

Simplify

i^{8} : (- 1)^{4}

= 125 (- 1)^{4} i

Simplify

(- 1)^{4} i : i

= 125 i

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Frequently Asked Questions (FAQ)

What is (5i^3)^3 ?
The solution to (5i^3)^3 is 125i