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Chapter 2: Problem 1

Write the given expression without exponents. $$x^{6}$$

Short Answer

Expert verified
x \times x \times x \times x \times x \times x

Step by step solution

01

Understand the Exponent

The exponent in the expression \(x^{6}\) tells us how many times the base \(x\) is multiplied by itself.
02

Apply the Exponent Rule

According to the exponent rule, \(x^{6}\) means \(x \times x \times x \times x \times x \times x\).
03

Write the Expression Without Exponents

Based on the rule, write the expression without exponents: \(x \times x \times x \times x \times x \times x\).

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Key Concepts

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

Exponents
An exponent refers to the number that shows how many times the base is multiplied by itself. In our example, the expression is written as \(x^{6}\), with 6 being the exponent.

When you see an exponent in a mathematical expression, it's telling you to multiply the base by itself, repeatedly, the number of times indicated by the exponent.

So, if the exponent is 3, as in \(x^{3}\), you multiply the base, which is \(x\), three times: \(x \times x \times x\).

This concept is key in algebra because it helps simplify expressions and makes calculations easier to manage.
Base
The base is the number or variable that is being multiplied by itself when raised to an exponent.

In the expression \(x^{6}\), the base is \(x\). This means that \(x\) is multiplied by itself 6 times.

Understanding what the base is really important. It tells you which number is being repeatedly used in the multiplication.

Think of the base as the building block of the expression. No matter how high the exponent, the base remains the number or variable that starts the repetitive multiplication process.

For instance, if you have \(y^{4}\), the base here is \(y\). So you would write it as \(y \times y \times y \times y\).
Multiplication
Multiplication in algebraic expressions can be broken down using exponents.

When you encounter an exponent, it's telling you to perform a series of multiplications.
In \(x^{6}\), you'd multiply the base, \(x\), by itself 6 times: \(x \times x \times x \times x \times x \times x\).

Multiplication is one of the basic arithmetic operations and is simply repeated addition; however, with exponents, this idea is extended to repeated multiplication.

Understanding how to expand exponent notation into basic multiplication helps you grasp the depth of algebraic simplifications.
  • Each multiplication step builds on the previous one.
  • It simplifies lengthy expressions into a more compact form.
  • Helps dealing with higher powers efficiently.

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Most popular questions from this chapter

Evaluate the given expression for \(x=0.24\) and \(y=-0.5 .\) Round off to the nearest thousandth where necessary. $$8.4 x-0.03 y$$

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$(x y z)^{2}$$

Simplify by combining like terms whenever possible. $$-3 x^{2}+5 x y-x y-x^{2}-2 x^{2}$$

Simplify each expression as completely as possible. $$5(y-3)+2[y-5(3-y)]$$

Examine each of the following expressions as given and determine the number of terms. Also find the coefficient and the literal part of each term. $$4 x^{2}-3 x+2$$
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