Evaluate the following powers of i i . ( 3 i ) 4 \left(3i\right)^4

we're asked to evaluate the following power of I. We're given three I raised to the power of four. Now I need to make sure and distribute this four to both things that I have in parentheses here. So raising that three to the power of four and also I to the power of four. Now three to the power of four is three times three times three times three, which will give me 81. So I have 81 times I to the fourth power. Now you might remember this power of I off the top of your head, but if you don't, you can always write it out. This is I times I times I times I four times. But I times I or I squared is always going to be negative one. That's just the definition of our imaginary unit. And I have another pair of negative one here. So this is really negative one times negative one, which would give me positive one. So this is just 81 times one, which is just 81. And that's our power of I.

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Multiple Choice

Evaluate the following powers of $i$ .
$open paren 3 i close paren to the fourth power$

$81$

$negative 81$

$9$

$negative 9$

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Verified step by step guidance

Recognize that the expression to evaluate is $\left(3i\right)^4$, where $i$ is the imaginary unit with the property $i^2 = -1$.

Use the property of exponents to rewrite the expression as $\left(3i\right)^4 = 3^4 \cdot i^4$.

Calculate \$3^4$ by multiplying 3 by itself four times: $3 \times 3 \times 3 \times 3$.

Evaluate $i^4$ by using the fact that $i^2 = -1$, so $i^4 = \left(i^2\right)^2 = (-1)^2$.

Multiply the results from steps 3 and 4 together to find the value of $\left(3i\right)^4$.

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Struggling with Beginning & Intermediate Algebra?

Evaluate the following powers of ii.(3i)4\(\left\)(3i\(\right\))^4

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Evaluate the following powers of $i$ .
$open paren 3 i close paren to the fourth power$