/*! 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 15 Find the value of c in each equa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 15

Find the value of c in each equation. $$\sqrt[4]{1}=c$$

Short Answer

Expert verified
c = 1

Step by step solution

01

Understand the Equation

The given equation is \[ \sqrt[4]{1} = c \]. This means we need to find some number c that, when raised to the power of 4, equals 1.
02

Recall the Fourth Root

The fourth root of a number \[ x \] is a number that, when raised to the power of 4, equals \[ x \].
03

Solve the Equation

We know that \[ 1^4 = 1 \]. Therefore, the value of \[ c = 1 \] because \[ 1^4 = 1 \].

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.

Fourth Root
When we talk about the fourth root of a number, we are looking for a value that, when raised to the fourth power, gives us the original number. In other words, the fourth root of a number \(x\) is a number \(y\) such that \(y^4 = x\). For example, the fourth root of 16 is 2, because \(2^4 = 16\). Similarly, the fourth root of 1 is 1, because \(1^4 = 1\). This concept is fundamental when solving equations that involve radicals and exponents. Remember, the fourth root is just one type of root, there are also square roots, cube roots, and so on.
Algebra
Algebra is a branch of mathematics that uses symbols, letters, and numbers to represent relationships and solve equations. In algebra, we often work with variables to generalize mathematical expressions and equations. For instance, in the given exercise, \(c\) is a variable we need to solve for. The equation is \(\textstyle{\textbackslash}frac{{1}}{4}{1}={c}\), which simplifies to \(c = 1\).When solving algebraic equations, it is essential to understand the operations and their properties. Here are some key points:
  • Equations should be balanced, meaning what is done to one side must be done to the other.
  • Know the inverse operations, like subtraction for addition or division for multiplication.
  • Simplify complicated expressions step by step.
Algebra plays a significant role in all levels of mathematics, helping us understand and describe patterns and relationships.
Exponents
Exponents are a way to represent repeated multiplication of the same number by itself. For example, \(2^3\) means \(2 \times 2 \times 2 = 8\). The number 2 is the base, and 3 is the exponent, indicating how many times the base is multiplied by itself. Here are some properties of exponents to remember:
  • Any number raised to the power of zero is 1, \(x^0 = 1\).
  • Multiplying numbers with the same base: \(a^m \times a^n = a^{m+n}\).
  • Dividing numbers with the same base: \(\frac{a^m}{a^n} = a^{m-n}\).
  • Raising a power to a power: \((a^m)^n = a^{mn}\).
In the exercise, the fourth root is essentially using exponents because the fourth root of 1 can be written as \(1^{\frac{1}{4}}\), and we know from exponent rules that \(1\) raised to any power is still \(1\). Understanding how exponents work is crucial for solving various mathematical problems.

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 value of m in each equation. $$ \sqrt[3]{1,331}=m $$

Ninety-six square tiles cover a 6 -foot-by- 12 -foot area. a. Write an equation that would help you find the side length of a tile, \(s .\) b. What is the side length of one of the tiles, in inches?

Complete Parts a鈥揺. a. Explain the rule in words. b. Find the coordinates of each vertex, and copy the figure onto graph paper. c. Perform the given rule on the coordinates of each vertex to find the image vertices. d. On the same set of axes, plot each image point. Connect them in order. e. Compare the image to the original: is it a reflection, a rotation, a translation, or some other transformation? Rule: \((x, y) \rightarrow(-x,-y)\)

What would you get if you used the coordinate method to dilate a picture by a factor of 0?

Consider what happens when you rotate a linear graph \(180^{\circ} .\) a. Graph the line \(y=2 x+4\) b. On the same grid, draw the image of the line under a \(180^{\circ}\) rotation centered at the origin. c. What do you notice about the image line and the original line? d. Write an equation of the new line. e. Does your equation in Part d support your observation in Part c? Explain.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics 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.