/*! 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 Evaluate the expression when \(x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 15

Evaluate the expression when \(x=3\) $$ 10^{x} $$

Short Answer

Expert verified
Therefore, the value of the expression \(10^x\) when \(x=3\) is 1000.

Step by step solution

01

Substitute the Given Value

Replace \(x\) in the equation \(10^x\) with the given value, which in this case is 3. So, the equation becomes \(10^3\).
02

Evaluate the Exponential Expression

\(10^3\) means '10 multiplied by itself 3 times'. In other words, it's \(10 * 10 * 10\), which equals to 1000.

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 unique way to express repeated multiplication of the same number. When we see an exponent, like in the expression \(10^3\), it tells us how many times to multiply the base number (10, in this case) by itself. The small number above and to the right (the exponent) is the number of times you perform this multiplication.Key things to remember about exponents:
  • The base is the number that is being multiplied.
  • The exponent indicates how many times the base is multiplied by itself.
  • In \(10^3\), the base is 10, and the exponent is 3, meaning \(10 \times 10 \times 10\).
Exponents are powerful tools for simplifying expressions and are often used in scientific notation, technology, and various fields of mathematics and science.
Substitution
Substitution is a technique used in algebra where we replace variables with their given values or known quantities.In the exercise, substitution involves replacing \(x\) with the number 3 in the expression \(10^x\). By substituting, we transform the general expression into a specific numerical one, \(10^3\), which can then be easily evaluated.To effectively use substitution:
  • Identify the variable in the expression.
  • Replace the variable with the value provided.
  • Ensure every instance of the variable is replaced to maintain consistency.
Substitution simplifies expressions, making them solvable and easier to understand.
Mathematical Operations
Mathematical operations are fundamental in solving expressions. They include addition, subtraction, multiplication, division, and exponentiation.In evaluating expressions like \(10^3\), our primary mathematical operation is exponentiation, which involves repeated multiplication.Steps to evaluate an expression using mathematical operations:
  • Identify the operations present in the expression, such as exponents or basic arithmetic.
  • Follow the order of operations (PEMDAS/BODMAS) to ensure accurate results. This means dealing with Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division, and finally Addition and Subtraction.
  • Carry out the operations step by step until the expression is completely simplified.
Understanding mathematical operations allows for precise and correct computation of expressions like \(10^3\).

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

Evaluate the expression. $$7[(18-6)-6]$$

Evaluate the expression for the given value of the variable. $$\frac{9}{10} \cdot y-\frac{3}{10} \text { when } y=\frac{1}{2}$$

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) A car travels 60 miles per hour for a distance of 300 miles. How long did the trip take?

Evaluate the expression for the given value of the variable. $$\frac{4}{5} \div n+13 \text { when } n=\frac{1}{5}$$

You plan to start your own greeting card business. Your startup cost of buying a computer and color printer is \(\$ 1400 .\) You also want to run an ad for \(\$ 50\) a week for 4 weeks. You plan to sell each card for \(\$ 1.79\). How many cards must you sell to equal or exceed your initial costs? Write an inequality that models the situation. Solve the inequality to find the minimum number of cards you must sell.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

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.