Evaluate each expression for p=−4p=-4, q=8q=8, and r=−10r=-10. 3p+3(4+p)3r+8\frac{3p + 3(4 + $$p)^3$$}{r + 8} r+83p+3(4+p)3

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

All textbooks

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 111

Chapter 1, Problem 111

Evaluate each expression for $p = - 4$ , $q equals 8$ , and $r = - 10$ . $\frac{3p + 3(4 + p)^3}{r + 8}$

Verified step by step guidance

First, substitute the given values into the expression: replace $ p $ with $ -4 $, $ q $ with $ 8 $ (though $ q $ is not used in this expression), and $ r $ with $ -10 $. The expression becomes $ 3(-4) + \frac{3(4 + (-4))^3}{-10 + 8} $.

Simplify inside the parentheses: calculate $ 4 + (-4) $ which simplifies to $ 0 $.

Evaluate the exponent: raise the result from step 2 to the power of 3, so calculate $ 0^3 $.

Calculate the numerator and denominator separately: multiply $ 3 $ by $ p $ (which is $ -4 $) for the first term, and multiply $ 3 $ by the result of the exponentiation for the numerator of the fraction. Then simplify the denominator by adding $ r $ and $ 8 $.

Finally, combine the terms by adding the first term and the fraction, and simplify the expression to get the final value.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Order of Operations

The order of operations dictates the sequence in which parts of an expression are evaluated: parentheses first, then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction. This ensures consistent and correct evaluation of expressions.

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. This step is essential to evaluate algebraic expressions for specific values, allowing the expression to be simplified to a numerical result.

Exponentiation

Exponentiation is the operation of raising a base number to a power, indicating repeated multiplication. Understanding how to correctly compute powers, especially with negative bases or sums inside parentheses, is crucial for accurate evaluation.

Recommended video:

6:13

Exponential Functions

Related Practice

Textbook Question

Calculate each value mentally. (24²)(0.5²)

926

views

Textbook Question

Perform the indicated operations. Assume all variables represent positive real numbers. $$\sqrt$[4]{81x^6y^3} - $\sqrt$[4]{16x^{10}y^3}$

903

views

Textbook Question

Multiply or divide as indicated. 78.65 ÷ 11

1048

views

Textbook Question

Multiply or divide as indicated. 0.07 × 0.004

1188

views

Textbook Question

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. {x | x ∈ M or x ∈ Q}

1028

views

Textbook Question

Let A = { -6, - 12/4 , - 5/8 , - √3, 0, 1/4 , 1, 2π, 3, √12}. List all the elements of A that belong to each set. Natural numbers

1043

views

Evaluate each expression for p=−4p=-4, q=8q=8, and r=−10r=-10. 3p+3(4+p)3r+8\(\frac{3p + 3(4 + p)^3}{r + 8}\)r+83p+3(4+p)3

Verified video answer for a similar problem:

Key Concepts

Order of Operations

Substitution of Variables

Exponentiation

Evaluate each expression for $p = - 4$ , $q equals 8$ , and $r = - 10$ . $\frac{3p + 3(4 + p)^3}{r + 8}$