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Popular >

simplify (3i^5)^2

Solution

simplify

(3 i^{5})^{2}

Solution

- 9

Solution steps

(3 i^{5})^{2}

Apply exponent rule:

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

(3 i^{5})^{2} = 3^{2} (i^{5})^{2}

= 3^{2} (i^{5})^{2}

3^{2} = 9

= 9 (i^{5})^{2}

Apply exponent rule:

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

assuming

a \geq 0

(i^{5})^{2} = i^{5 \cdot 2}

= 9 i^{5 \cdot 2}

Multiply the numbers:

5 \cdot 2 = 10

= 9 i^{10}

Apply exponent rule:

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

i^{10} = (i^{2})^{5}

= 9 (i^{2})^{5}

Apply imaginary number rule:

i^{2} = - 1

= 9 (- 1)^{5}

(- 1)^{5} = - 1

= 9 (- 1)

Multiply the numbers:

9 (- 1) = - 9

= - 9

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Frequently Asked Questions (FAQ)

What is (3i^5)^2 ?
The solution to (3i^5)^2 is -9