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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 599 (page 857)

In the following exercises, simplify. Assume all variables are positive.
i¹⁷² $i^{172} .$

Short Answer

Expert verified

The solution of $i^{172} i s 1 .$

Step by step solution

01

Step 1. Given information

We have $i^{172} .$

02

Step 2. Divide the index by 4 and simplify

$i^{172} = i^{4 \times 43 + 0} i^{172} = 1^{43} = 1$

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Most popular questions from this chapter

Simplify:

a. ${(32 x^{\frac{1}{3}})}^{\frac{3}{5}}$ b. ${(x^{\frac{3}{4}} y^{\frac{1}{2}})}^{\frac{2}{3}}$

Simplify:

a. $x^{\frac{1}{6}} \cdot x^{\frac{4}{3}}$ b. ${(x^{6})}^{\frac{4}{3}}$ c. $\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}}$

Simplify: $\sqrt{\frac{48 x^{5}}{100}} .$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{72 n^{11}}}{\sqrt{2 n}}$

(b) $\sqrt[3]{\frac{162}{6}}$

(c) $\sqrt[4]{\frac{160 r^{10}}{5 r^{3}}}$

In the following exercises, solve.
$\sqrt{6 n + 1} + 4 = 8$

See all solutions

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