/*! 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 21 \(\left(6 \times 10^{3}\right)\l... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 21

\(\left(6 \times 10^{3}\right)\left(2 \times 10^{4}\right)\)

Short Answer

Expert verified
12 \times 10^7

Step by step solution

01

Multiply the coefficients

First, multiply the numerical coefficients of the two terms: \(6\) and \(2\). \(6 \times 2 = 12\)
02

Add the exponents

Next, add the exponents from the power of 10 terms: \(10^3\) and \(10^4\). Using the property of exponents \(a^m \times a^n = a^{m+n}\), \(10^3 \times 10^4 = 10^{3+4} = 10^7\)
03

Combine the results

Finally, combine the results from step 1 and step 2: \(12 \times 10^7\)

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.

Multiplying Coefficients
When multiplying terms in scientific notation, the first step is to multiply the coefficients. Coefficients are the numbers before the power of 10, like the 6 in \(6 \times 10^3\) or the 2 in \(2 \times 10^4\).

To do this, you simply multiply them like regular numbers. So for \(6 \times 2\), you get 12.

This step is easy and only involves simple multiplication. Breaking your problem into smaller parts can make it more manageable.
Adding Exponents
The next step is to add the exponents. When you multiply numbers with the same base, you add their exponents according to the property \(a^m \times a^n = a^{m+n}\).

In our example, the base is 10, and we have \(10^3\) and \(10^4\). Adding the exponents, 3 and 4, gives us 7. So, \(10^3 \times 10^4 = 10^7\).

Remember, this only works because the base (10) is the same for both terms. If the bases were different, this rule wouldn鈥檛 apply.
Properties of Exponents
Understanding the properties of exponents is crucial for simplifying expressions. Some important properties to remember are:
  • \(a^m \times a^n = a^{m+n} \) (When multiplying like bases, you add the exponents)
  • \(\frac{a^m}{a^n} = a^{m-n} \) (When dividing like bases, you subtract the exponents)
  • \( (a^m)^n = a^{mn} \) (When raising a power to another power, you multiply the exponents)
  • \( a^0 = 1 \) (Any number raised to the zero power is 1)


These rules make it easier to handle and simplify complex expressions. Always keep them in mind when working with exponents.

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

A customer borrows \(\$ 8500\) for 6 years at a simple interest rate of \(11.3 \%\). Find the simple interest.

\(\left(x^{2}+10 x+16\right) \div(x+8)\)

\(\left(2 x^{2}+11 x+15\right) \div(x+3)\)

Problem: Simplify: \((5 x-2)(x-3)\) Incorrect Answer: \((5 x-2)(x-3)\) $$ \begin{aligned} &=5 x(x)+5 x(-3)-2 x-2(3) \\ &=5 x^{2}-15 x-2 x-6 \\ &=5 x^{2}-17 x-6 \end{aligned} $$

\(\left(2 x^{2}+9 x+20\right) \div(x+4)\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.