What is i^{29}*i^{27}*i^{30} ?

The solution to i^{29}*i^{27}*i^{30} is -1

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simplify i^{29}i^{27}i^{30}

simplify

i^{29} \cdot i^{27} \cdot i^{30}

- 1

Solution steps

i^{29} i^{27} i^{30}

Apply exponent rule:

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

i^{29} i^{27} i^{30} = i^{29 + 27 + 30}

= i^{29 + 27 + 30}

Add the numbers:

29 + 27 + 30 = 86

= i^{86}

Apply exponent rule:

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

i^{86} = (i^{2})^{43}

= (i^{2})^{43}

Apply imaginary number rule:

i^{2} = - 1

= (- 1)^{43}

(- 1)^{43} = - 1

= - 1

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