/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 Write an equivalent expression u... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 33

Write an equivalent expression using exponential notation. $$ \sqrt{17} $$

Short Answer

Expert verified
17^{\frac{1}{2}}

Step by step solution

01

Understanding the Given Expression

The given expression is the square root of 17, which can be written as \( \sqrt{17} \).
02

Square Root in Exponential Notation

In exponential notation, the square root of a number can be expressed as the number raised to the power of \( \frac{1}{2} \).
03

Convert the Expression

Convert the given expression \( \sqrt{17} \) to exponential notation by raising 17 to the power of \( \frac{1}{2} \). The equivalent expression is \[ 17^{\frac{1}{2}} \].

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Square Roots
A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 脳 3 = 9. In mathematical notation, the square root of a number is represented using the radical symbol, like this: \( \sqrt{9} \).
In the case of the number 17, the square root is written as \( \sqrt{17} \). This means we are looking for a number which, when squared (multiplying the number by itself), equals 17.
Square roots can also be expressed using exponents, which leads us to the next core concept.
Exponents and Their Role
Exponents are a way of representing repeated multiplication. An exponentiation expression consists of a base and an exponent, written as \( a^b \). Here, 'a' is the base and 'b' is the exponent. For example, in the expression \( 2^3 \), 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself three times: 2 脳 2 脳 2 = 8.
Now, think about the square root of 17 in terms of exponents. The square root of a number can be represented as the number raised to the power of \( \frac{1}{2} \). So, \( \sqrt{17} \) becomes \( 17^{\frac{1}{2}} \). This is because raising a number to the power of \( \frac{1}{2} \) is the same as taking the square root of that number.
Algebraic Expressions Simplified
Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. Variables are symbols that represent unknown values and generally use letters like x, y, z, etc.
In algebra, we often simplify expressions to make them easier to handle. Simplifying means rewriting the expression in a way that is easier to understand or more concise.
For instance, our original expression \( \sqrt{17} \) is simplified into exponential form as \( 17^{\frac{1}{2}} \). This not only makes the expression more compact but also helps when applying more advanced algebraic manipulations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find a simplified form for \(f(x) .\) Assumex \(\geq 0\). $$\begin{aligned}&f(x)=\sqrt{20 x^{2}+4 x^{3}}-3 x \sqrt{45+9 x}+\\\&\sqrt{5 x^{2}+x^{3}}\end{aligned}$$

Simplify. $$ \frac{i^{5}+i^{6}+i^{7}+i^{8}}{(1-i)^{4}} $$

Simplify. $$7 x \sqrt{(x+y)^{3}}-5 x y \sqrt{x+y}-2 y \sqrt{(x+y)^{3}}$$

Find a simplified form for \(f(x) .\) Assumex \(\geq 0\). $$f(x)=\sqrt[4]{16 x^{4}+16 x^{5}}-2 \sqrt[4]{x^{8}+x^{9}}$$

To prepare for Section \(10.6,\) review solving equations (Sections 2.2 and 7.6 and Chapter 6 ). Solve. $$9 x^{2}-6 x+1=7+5 x-x^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.