/*! 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 11 In Exercises \(1-28\), compute t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 11

In Exercises \(1-28\), compute the numbers. $$ (.000001)^{1 / 3} $$

Short Answer

Expert verified
0.01

Step by step solution

01

Understand the Problem

The given exercise is \((.000001)^{1 / 3}\). This means we need to find the cube root of 0.000001.
02

Rewrite the Number in Scientific Notation

Rewrite \(.000001\) as a power of 10. In scientific notation, \(.000001\) is \(1 \times 10^{-6}\).
03

Apply the Exponent Rule

Use the exponent rule that states \((a^{b})^{c} = a^{bc}\). Here, \((1 \times 10^{-6})^{1 / 3} = 1^{1 / 3} \times (10^{-6})^{1 / 3}\).
04

Simplify the Calculations

Simplify each part separately. \(1^{1 / 3} = 1\), and \((10^{-6})^{1 / 3}\) is \(10^{-6 \times 1 / 3} = 10^{-2}\).
05

Combine the Results

Multiply the simplified values back together: \(1 \times 10^{-2} = 0.01\).

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.

Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a more compact and readable form. It is especially useful in fields like science and engineering, where such numbers are common. In scientific notation, a number is written as a product of two parts: a decimal number between 1 and 10, and a power of 10. For example, instead of writing 0.000001, we write it as
  • 1 脳 10^{-6}
This makes it easier to see the magnitude of the number at a glance. In our exercise, we converted 0.000001 to 1 脳 10^{-6}. This step is essential because it allows us to simplify the calculation using exponent rules.
Exponent Rules
Exponent rules, also known as laws of exponents, are fundamental principles that govern operations involving exponents. One important exponent rule is (a^b)^c = a^{bc}. This rule is particularly useful for simplifying expressions where exponents are involved.Let's apply this rule to our example:
  • We have (1 脳 10^{-6})^{1 / 3}
Using the exponent rule,
  • we can separate this into (1^{1 / 3} 脳 (10^{-6})^{1 / 3})
The next part is straightforward:
  • 1^{1 / 3} remains 1 because any number raised to any power still equals 1.
  • To calculate (10^{-6})^{1 / 3}, we multiply the exponents: -6 * 1/3 = -2. So, (10^{-6})^{1 / 3} = 10^{-2}.
Simplifying Expressions
Simplifying mathematical expressions involves reducing them to their simplest and most manageable form. This often includes applying exponent rules as well as basic arithmetic principles.In the final steps,
  • we combined the values we obtained: (1^{1 / 3}) 脳 (10^{-6})^{1 / 3}
This simplifies to:
  • 1 脳 10^{-2}
By multiplying these results together, we end up with a much simpler number:
  • 0.01
Thus, the cube root of 0.000001 is simplified to 0.01. Mastering this process of simplifying expressions can greatly ease solving complex algebraic problems and help in various branches of math and science.

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

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. \(\frac{1}{y x^{-5}}\)

Let \(f(x)=x^{2}\). Graph the functions \(f(x)+1, f(x)-1, f(x)+2\), and \(f(x)-2 .\) Make a guess about the relationship between the graph of a general function \(f(x)\) and the graph of \(f(x)+c\) for some constant \(c\). Test your guess on the functions \(f(x)=x^{3}\) and \(f(x)=\sqrt{x}\).

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. \(\left(16 x^{8}\right)^{-3 / 4}\)

Use the laws of exponents to compute the numbers. \(\frac{10^{4}}{5^{4}}\)

Compute the numbers. \(9^{1.5}\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.