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Chapter 1: Problem 96

\(4^{3}+4 \cdot 6 \div(-4-2)\)

Short Answer

Expert verified
60

Step by step solution

01

Calculate the exponent

First, calculate the exponent part of the expression. We have: \(4^3 = 4 \times 4 \times 4 = 64\)
02

Calculate the parentheses

Next, calculate the value inside the parentheses: \(-4 - 2 = -6\)
03

Perform the multiplication and division

Now perform the multiplication and division before addition as per the order of operations.\(4 \times 6 = 24\)\(24 \div -6 = -4\)
04

Perform the addition

Finally, add the results obtained from the exponentiation and the division steps:\(64 + (-4) = 60\)

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Key Concepts

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

Exponents
Exponents are a core part of mathematics. They tell us how many times to multiply a number by itself.
For example, in the expression given, we had to evaluate an exponent: \(4^3\).
To break this down:
- Start with 4.
- Multiply 4 by itself three times: \(4 \times 4 \times 4 = 64\).
Exponents rapidly increase the value of numbers. Always handle them early in calculations.
They are part of the PEMDAS/BODMAS order of operations.
Parentheses
Parentheses are essential as they determine the immediate operations to perform.
They help us group parts of our expressions.
Considering our example, we had \((-4 - 2)\).
Begin by solving what鈥檚 inside the parentheses.
- Here, -4 minus 2 equals -6:
So, \((-4 - 2) = -6\).
Parentheses ensure that certain operations are completed before others, making them crucial in calculations.
Multiplication and Division
Multiplication and division must be performed from left to right.
After determining the value inside the parentheses, we proceed with these operations.
- First, multiply 4 by 6 to get 24: \(4 \times 6 = 24\).
- Next, divide 24 by -6: \(24 \div -6 = -4\).
These operations are prioritized above addition and subtraction in the order of operations.
Addition
Addition is usually the final step in our order of operations.
In our specific example, we were left with an addition after completing the other operations.
We had to add 64 and -4: \(64 + (-4) = 60\).
Always perform addition (and subtraction) last unless grouped by parentheses.
This final step gives us our answer.

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Most popular questions from this chapter

\(\frac{12 \mathrm{~km}}{2 \mathrm{~km}}\)

The intensity of \(\mathrm{X}\)-ray radiation depends on the distance from the source of radiation. If the distance from the source of radiation changes from \(D_{1}\) to \(D_{2}\), the intensity changes from intensity \(I_{1}\) to \(I_{2}\). The formula for finding the new intensity is \(I_{2}=\frac{I_{1} \cdot\left(D_{1}\right)^{2}}{\left(D_{2}\right)^{2}}\). When \(D_{1}\) is \(25 \mathrm{~m}\), the intensity \(I_{1}\) is 620 roentgen per hour. Find the intensity of radiation \(I_{2}\) if \(D_{2}\) is \(5 \mathrm{~m}\).

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