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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 577. (page 856)

In the following exercises, simplify.
$i^{48}$

Short Answer

Expert verified

The simplified form is $1$ .

Step by step solution

01

Step 1. Given information.

The given imaginary number is $i^{48}$ .

02

Step 2. Simplify the power.

We know that,

$i = \sqrt{- 1} i^{2} = - 1 i^{3} = - i i^{4} = 1$

Divide the power by 4 and rewrite,

$i^{48} = {(i^{4})}^{12} = {(1)}^{12} = 1$

03

Step 3. Conclusion.

Therefore, the simplified form is $1$ .

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Most popular questions from this chapter

In the following exercises, solve.
$\sqrt{12 u + 1} - 11 = 0$

Simplify:

(a) $4^{\frac{3}{2}}$

(b) $27^{- \frac{2}{3}}$

(c) $625^{- \frac{3}{4}}$

Simplify:

$(a) \sqrt{180 m^{9} n^{11}} (b) \sqrt{72 x^{6} y^{5}} (c) \sqrt{80 x^{7} y^{4}} .$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{45 p^{9}}}{\sqrt{5 q^{2}}}$

(b) $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$

(c) $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{2}}}$

Explain why $\sqrt[4]{- 64}$ is not a real number but $\sqrt[3]{- 64}$ is.

See all solutions

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