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Chapter 1: Problem 26

Evaluate each expression. $$ 6^{4} $$

Short Answer

Expert verified
\(6^4 = 1296\)

Step by step solution

01

Understanding the Exercise

The exercise asks you to evaluate the expression \(6^4\). This means we need to calculate the value of 6 raised to the power of 4.
02

Calculating the Power

Begin by recognizing that raising a number to the power of 4 means multiplying the number by itself three more times. Hence, \(6^4 = 6 \times 6 \times 6 \times 6\).
03

First Multiplication

Calculate \(6 \times 6\). This equals 36.
04

Second Multiplication

Multiply the result by another 6: \(36 \times 6 = 216\).
05

Final Multiplication

Finally, multiply 216 by another 6: \(216 \times 6 = 1296\).

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Key Concepts

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

Understanding Powers and Exponents
When we talk about powers, we're referring to a way of expressing repeated multiplication of the same number. In mathematical terms, we use exponents to denote this concept. An expression like \(6^4\) is read as "six raised to the power of four." The number 6 is known as the base, and 4 is the exponent.
  • The exponent tells us how many times to multiply the base by itself.
  • For example, \(6^4\) means we multiply 6 by itself 4 times: \(6 \times 6 \times 6 \times 6\).
  • This may seem complex at first, but it's just an efficient method to denote repeated multiplication.
Practically speaking, understanding powers helps with simplifying expressions and solving larger mathematical problems. Becoming familiar with the basic characteristics of powers can make math much simpler and more intuitive.
Mastering Multiplication of Numbers
Multiplication is a fundamental mathematical operation that involves adding a number to itself a certain number of times. When dealing with powers, as in \(6^4\), multiplication becomes especially important.
  • Begin by multiplying 6 by itself, causing us to first calculate \(6 \times 6 = 36\).
  • Next, continue multiplying the result by 6 to carry out the expression, so: \(36 \times 6 = 216\).
  • Finish by multiplying once more by the base, \(216 \times 6 = 1296\).
Each step simplifies the expression further, taking us closer to the final value. This method ensures you systematically arrive at the correct answer, demonstrating how multiplication underlies the concept of powers.
Evaluating Expressions with Confidence
Evaluating expressions such as \(6^4\) might seem daunting initially, but following a structured approach helps. Evaluation means calculating the numerical value of a mathematical expression by following specific procedures.
  • First, identify the operation required鈥攊n this case, raising a number to a power.
  • Then execute the operations step by step, carefully multiplying the numbers as guided by the power.
  • Finally, double-check the computations to ensure accuracy, arriving at the expression's evaluated value.
By breaking down the evaluation process into simpler steps, you can tackle similar mathematical expressions with confidence and improved problem-solving skills. This structured method is not only useful for solving exponent-related problems but also assists in a variety of mathematical computations.

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Most popular questions from this chapter

NASCAR. Complete the table below to determine how many points the third and fourth place finishers were behind the leader. $$ \begin{array}{|c|c|c|c|} \hline & {2009 \text { Final Driver Standings }} & {} & {} \\ \hline & {} & {\text { Points }} & {\text { Points behind }} \\ \hline \text { Rank } & {\text { Driver }} & {} & {\text { leader }} \\ \hline 1 & {\text { Jimmie Johnson }} & {6,652} & {. .} \\ \hline 2 & {\text { Mark Martin }} & {6,511} & {-141} \\ \hline 3 & {\text { Jeff Gordon }} & {6,473} & {} \\ \hline 4 & {\text { Kurt Busch }} & {6,446} & {} \\ \hline \end{array} $$

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