/*! 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 40 Use the laws of exponents to com... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 40

Use the laws of exponents to compute the numbers. $$\left(6^{1 / 2}\right)^{0}$$

Short Answer

Expert verified
1

Step by step solution

01

Understand the problem

Given the expression \(\big(6^{1/2}\big)^{0}\), use the laws of exponents to simplify it.
02

Apply exponent zero law

According to the exponent zero law, any number raised to the power of zero is always 1. Thus, applying this law to \(\big(6^{1/2}\big)^{0}\): \(\big(6^{1/2}\big)^{0} = 1\).

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.

Exponent Zero Law
When dealing with exponential expressions, a fundamental rule to know is the Exponent Zero Law. This law states that any non-zero number raised to the power of zero equals 1. It doesn't matter how large or complex the number is, or even if it is a fraction or a decimal. If the exponent is zero, the entire expression simplifies to 1.
For example, let's consider the expression \(x^0\). According to the Exponent Zero Law, this simplifies directly to 1, regardless of the value of \(x\) as long as it isn't zero.
This rule helps make calculations simpler and is pivotal in algebra and higher-level math.
Simplification
The process of simplification in mathematics means breaking down a complex expression into its most basic form. Simplification often requires a good grasp of the laws governing the mathematical operations being performed.
In the context of exponents, simplification involves using exponent rules to condense and solve expressions. For our exercise, we begin with \( \big(6^{1/2} \big)^{0} \). Using the Exponent Zero Law, we know that this expression simplifies directly to 1, as explained before.
Always remember to double-check your steps when simplifying, ensuring you've applied the appropriate laws correctly.
Exponential Expressions
Understanding exponential expressions is crucial in mastering exponent laws. An exponential expression is any mathematical expression involving a base and an exponent. The base can be any number, and the exponent indicates how many times the base should be multiplied by itself.
For instance, in the expression \(2^3\), 2 is the base, and 3 is the exponent, meaning \(2 \times 2 \times 2 = 8\).
In our exercise, the expression \( \big(6^{1/2} \big)^{0} \) involves a more complex base of \(6^{1/2}\). Note even with complex bases, the laws of exponents, like the Exponent Zero Law, still apply.
Mastering these principles provides a strong foundation for more advanced mathematical topics.

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 the points of intersection of the graphs of the functions. (Use the specified viewing window.) $$f(x)=2 x-1 ; g(x)=x^{2}-2 ;[-4,4] \text { by }[-6,10]$$

If \(g(t)=4 t-t^{2},\) find \(\frac{g(t+h)-g(t)}{h}\) and simplify.

Let \(f(x)=x^{6}, g(x)=\frac{x}{1-x},\) and \(h(x)=x^{3}-5 x^{2}+1 .\) Calculate the following functions. $$h(g(x))$$

The expressions may be factored as shown. Find the missing factors. $$2 x^{2 / 3}-x^{-1 / 3}=x^{-1 / 3}(\quad)$$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. $$\frac{1}{x^{-3}}$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.