Question

standard form of i^8/3i^-27

Answer 1

Answer:

i/-3

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given:

$\frac{ {i}^{8} }{3 {i}^{ - 27} }$

To find : Write in standard form.

Solution:

Tip:

${i}^{4} = 1$

${i}^{2} = - 1$

and

${i}^{3} = - i$

Simplify the expression.

$\frac{ {i}^{8} }{3 {i}^{ - 27} } = \frac{({ {i}^{4}) }^{2} }{3 \times \frac{1}{( {i}^{4})^{6} \times {i}^{3} } }$

or

$\frac{ {i}^{8} }{3 {i}^{ - 27} } = \frac{({ 1) }^{2} }{3 \times \frac{1}{( 1)^{6} \times {i}^{3} } }$

or

$\frac{ {i}^{8} }{3 {i}^{ - 27} } = \frac{({ i) }^{3} }{3 }$

or

$\frac{ {i}^{8} }{3 {i}^{ - 27} } = \frac{ - i}{3}$

convert into standard form

$\frac{ {i}^{8} }{3 {i}^{ - 27} } = 0 - i\frac{ 1}{3}$

Final answer:

$\bf \frac{ {i}^{8} }{3 {i}^{ - 27} } = 0 - i\frac{ 1}{3}$

Hope it helps you.

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