Problem 66 Simplify. $$ 15(23-4 \cdot 2... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 1: Problem 66

Simplify. $$ 15(23-4 \cdot 2)^{3} \div(3 \cdot 25) $$

Short Answer

Expert verified

675

Step by step solution

Simplify the expression inside the parentheses

First, simplify inside the parentheses: $23 - 4 \times 2$Multiply before subtracting: $4 \times 2 = 8$Now subtract: $23 - 8 = 15$So, the expression simplifies to:$15(15)^{3} e (3 \times 25)$

Simplify the exponent

Next, simplify the exponent, $(15)^{3}$:Multiply 15 three times: $15 \times 15 \times 15 = 3375$So, the expression now is: $15 \times 3375 e (3 \times 25)$

Perform the multiplication and division

Next, multiply 15 with 3375: $15 \times 3375 = 50625$Now, simplify the denominator: $3 \times 25 = 75$Finally, divide: $50625 e 75 = 675$

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.

Order of Operations

Understanding the order of operations is crucial in simplifying expressions correctly. The order determines which operations to perform first. A common acronym to remember this is PEMDAS:

P: Parentheses
E: Exponents
MD: Multiplication and Division (left to right)
AS: Addition and Subtraction (left to right)

For example, in the exercise: $ 15(23-4 \times 2)^{3} \div (3 \times 25) $
We first simplify inside the parentheses, then handle the exponent. Next, multiply and divide in sequence.

Parentheses

Parentheses group parts of an expression that should be handled first. Always simplify expressions inside parentheses before moving on to other operations. In our exercise, we start by simplifying: $ 23 - 4 \times 2 $
Here, 4 and 2 are multiplied to get 8. Then subtract 8 from 23, resulting in 15. Thus, the expression updates to: $(15)^{3} \div (3 \times 25) $

Exponents

Exponents indicate repeated multiplication of a number by itself. The expression $(15)^{3}$ means multiplying 15 three times: $15 \times 15 \times 15 = 3375$.
After handling the parentheses, we simplify the exponent part next: $15 \times 3375$. At this point, our expression becomes simpler: \15 \times 3375 \div (3 \times 25)\.

Multiplication and Division

These operations are performed after parentheses and exponents, moving from left to right. In our case, we multiply 15 by 3375 first: $15 \times 3375 = 50625$.
Next, simplify the denominator: $3 \times 25 = 75$
Finally, divide 50625 by 75: $50625 \div 75 = 675$.
Hence, the simplified expression is 675.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify. $$ 15(23-4 \cdot 2)^{3} \div(3 \cdot 25) $$

Short Answer

Step by step solution

Simplify the expression inside the parentheses

Simplify the exponent

Perform the multiplication and division

Key Concepts

Order of Operations

Parentheses

Exponents

Multiplication and Division

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Mechanics Maths

Probability and Statistics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.