/*! 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 110 Simplify each expression using t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 110

Simplify each expression using the Product Property for Exponents. $$m^{x} \cdot m^{3}$$

Short Answer

Expert verified
The simplified expression is \(m^{x+3}\).

Step by step solution

01

- Understand the Product Property of Exponents

The Product Property of Exponents states that when multiplying two expressions with the same base, you add the exponents: Formula: Formula: Formula: Formula: \(a^m \times a^n = a^{m+n}\) The Product Property of Exponents states that when you multiply two expressions with the same base, you add their exponents. For example, \(a^m \times a^n = a^{m+n}\).
02

- Identify the Base and Exponents

The base in the given expression is \(m\), and the exponents are \(x\) and \(3\).
03

- Apply the Product Property of Exponents

Use the product property to add the exponents together: \( m^x \times m^3 = m^{x+3} \).
04

- Simplified Expression

The expression \(m^x \times m^3\) simplifies to \(m^{x+3}\).

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.

Exponents
Exponents are a way to show repeated multiplication of a number by itself. For example, in the expression \(a^m\), 'a' is called the base, and 'm' is the exponent. The exponent tells us how many times we multiply the base by itself.
\(a^2\) means \(a \times a\), while \(a^3\) means \(a \times a \times a\).
This concept helps simplify large multiplications and is fundamental in algebra.
Simplifying Expressions
Simplifying expressions is a key skill in algebra. It involves rewriting an expression in its simplest form. When dealing with exponents, one important property to know is the Product Property of Exponents.
This property states: \(a^m \times a^n = a^{m+n}\).
Meaning, when you multiply two expressions with the same base, you simply add their exponents. For example:
  • \(x^2 \times x^3 = x^{2+3} = x^5\)
  • \(y^4 \times y^2 = y^{4+2} = y^6\)
By using this property, you can make complex expressions easier to handle.
Algebra Basics
Understanding the basics of algebra is crucial for solving mathematical problems. Algebra involves working with variables, constants, and arithmetic operations. A variable represents an unknown value, and it is usually denoted by a letter such as x, y, or m.
In algebra, you often use properties and rules to rearrange and simplify expressions. For instance, knowing the Product Property of Exponents helps when you see an expression like \(m^x \cdot m^3\). Here, 'm' is the base, and applying the property, you get:
  • \(m^x \cdot m^3 = m^{x+3}\)
Thus, understanding these fundamental rules allows you to manage and solve algebraic expressions efficiently.

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

Handshakes At a company meeting, every employee shakes hands with every other employee. The number of handshakes is given by the expression \(\frac{n^{2}-n}{2},\) where \(n\) represents the number of employees. How many handshakes will there be if there are 10 employees at the meeting?

Divide each polynomial by the monomial. $$\frac{46 x^{3}+38 x^{2}}{2 x^{2}}$$

Divide each polynomial by the monomial. $$\frac{20 y^{2}+12 y-1}{-4 y}$$

Divide each polynomial by the monomial. $$\frac{35 a^{4}+65 a^{2}}{-5}$$

Simplify. (a) \(2^{-8}\) (b) \(10^{-2}\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.