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Chapter 0: Problem 88

Evaluate each expression for \(a=-3, b=64,\) and \(c=6 .\) $$ -3 a^{4}-3 c $$

Short Answer

Expert verified
-261

Step by step solution

01

Substitute the Values

Replace the variables in the expression with their given values. Here, substitute \(a = -3\), \(c = 6\):\[-3 (-3)^{4} - 3 (6)\]
02

Evaluate the Exponent

Calculate \((-3)^{4}\). Since any negative number raised to an even power is positive, we get:\[(-3)^{4} = 81\]
03

Multiply Constants

Substitute back \(81\) into the expression and simplify the coefficients. Summarizing:\[-3 \times 81 - 3 \times 6\]Calculate each term:\[-3 \times 81 = -243\]\[-3 \times 6 = -18\]
04

Combine the Results

Add the results from the previous step:\[-243 - 18 = -261\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution in Algebra
In algebra, substitution is the act of replacing variables with their specific values. It helps simplify expressions and solve equations. For example, consider the exercise: evaluate egiven a = -3, b = 64, c = 6everthing in the expression equation Substitute the valuesReplace the variables with the given numbers: a = -3a = -3equationawith -3 and c C = 6 we it asequation a = -3 naturally provides an updated simpler expression . which looks like easy to calculate.to and proceed .
Exponent Rules
Understanding exponent rules is crucial in algebra. An exponent tells you how many times to multiply a number by itself. For example, in the equation means ais multiplied by itself four times to get This is as:Step For our exercisecalculated as 81.Remember some key exponent rules :
  • A negative baseswich raises same
  • the exponent .
  • value even, as in our case,Any even power will be straightforward .
and positive.Another important
  • Multiplication rule, exponents is.
  • different exampletimes each times if
variable multiplied
Multiplying Constants
When simplifying algebraic expressions, one often needs to multiply constants, which is a straightforward process. In our exercise,After we found 81 by raising - mentioned 3 to example the exponent 4.We must multiply the result by the constant:- -3 as per original formula:the term of-3 *81,- Thus, resultantcalculation 243.for another expression fromSimilarly,multiplication occurs same time3*same consonatsult is simple 18. simplified multiplication leads next step
Combining Results in Algebra
Once all individual calculations are complete, it's time to combine them. This involves addition or subtraction as necessary. In our exercise,we derived:- three -243 and -.separately were-18 termed combine summing up -operation is: straightforward:-243-18 leads sumultimately calculated as -261.The
This merging involves critical subtraction and of simplest termsamount complete mathematical algorithm process verification of accuracycalculationseasily - expected end.

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Most popular questions from this chapter

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