Question

Use a calculator to evaluate each expression. Round your answer to three decimal places. \(-(2.8)^{6}\)

Short answer

-481.890

Step-by-step solution

- Understand the expression

Identify that the expression to be evaluated is \(-(2.8)^6\). This means we need to raise 2.8 to the 6th power and then take the negative of that result.

- Calculate the base raised to the power

Using a calculator, calculate \(2.8^6\). Input 2.8 and then use the power function to raise it to the 6th power: 2.8^6.

- Apply the negative sign

Take the result from Step 2 and multiply by \(-1\). This gives \(-(2.8)^6\).

- Round the answer

Round the result obtained in Step 3 to three decimal places.

Key concepts

exponents

Exponents are a way to express repetitive multiplication. For example, 2^3 means multiplying 2 by itself three times: 2 * 2 * 2, which equals 8.When dealing with exponents, it’s crucial to understand the base (the number being multiplied) and the power (the number of times the base is multiplied).In the given exercise, the base is 2.8 and the power is 6. This means we multiply 2.8 by itself six times:

• 2.8 * 2.8 = 7.84
• 7.84 * 2.8 = 21.952
• 21.952 * 2.8 = 61.4656
• 61.4656 * 2.8 = 172.10368
• 172.10368 * 2.8 = 481.890304
• 481.890304 * 2.8 = 1349.292851

Using a calculator can simplify this process greatly.Just enter 2.8 and then use the power function (usually denoted as ^ or with a button like y^x).

negative numbers

Negative numbers are numbers less than zero. They are often represented with a minus sign (-) before them.In our exercise, after calculating 2.8^6, we need to apply the negative sign.This means we take the positive result and multiply it by -1. Understanding this step helps us know that :

• Positive Results: 481.890304
• Negative Results: -481.890304

This rule applies to any positive number multiplied by -1, making it a negative number.

mathematical rounding

Rounding is simplifying a number to make it easier to work with. We limit the number of decimal places while retaining the number's overall value.For example, rounding 3.14159 to three decimal places gives us 3.142.In the exercise, once we have our result -(2.8)^6, we get -481.890304. We focus on the number of decimal places specified (three).To do this:

• Look at the fourth decimal place.
• If it's 5 or more, we round up the third decimal place by one.
• If it's less than 5, we leave the third decimal place as is.

So, -481.890304 becomes -481.890 when rounded to three decimal places.

step-by-step problem solving

Solving math problems step-by-step helps break down complex calculations into manageable parts. Here’s a structured approach: Identify the problem: Understand what's being asked. In our case, it involves calculating -(2.8)^6 and rounding the result.Use tools: Use a calculator to find 2.8^6. It’s faster and reduces the risk of error.Apply operations: Apply the negative sign to the result.Round the final result: Simplify the number to the required decimal places.Each step should be done carefully to avoid mistakes. Following these steps ensures accuracy and clarity in problem solving.