Question

Use a calculator to evaluate each expression. Round your answer to three decimal places. \((2.2)^{-5}\)

Short answer

0.003

Step-by-step solution

Understand the Expression

The expression to evaluate is \( (2.2)^{-5} \). This means we need to find the value of raising 2.2 to the power of -5.

Enter the Expression into the Calculator

Power it on the calculator. Key in the base 2.2 followed by the exponent -5. On most calculators, you can enter this as \( 2.2 \), then press the exponent button (often labeled \( \text{EXP} \), \( \text{^} \), or similar), and finally key in -5.

Calculate the Expression

Press the equals button \( = \) to evaluate the expression. The calculator should now provide you with a value.

Round the Answer

The calculator's output may not be rounded to three decimal places. Look at the given value and round it to three decimal places. For instance, if the output is 0.002915451896, round it to 0.003.

Key concepts

negative exponents

Negative exponents can seem confusing at first, but they are quite simple. When you see an expression like \(x^{-n}\), it means \(1/x^n\).
So, raising a number to a negative exponent is equivalent to taking the reciprocal of that number raised to the positive exponent. In our example, \( (2.2)^{-5} \) is the same as \( 1 / (2.2)^5 \).
Negative exponents tell us how many times to divide 1 by that number. Understanding this can make evaluating such expressions less daunting.

using calculators for math

Calculators are valuable tools for solving math problems quickly and accurately.
Here’s how you can use a calculator to solve expressions with exponents:

• First, power it on and ensure it's set to the correct mode. For standard arithmetic, you’ll need it set to normal mode, not scientific or programming mode.
• Second, enter the base number. For \( (2.2)^{-5} \), you would key in 2.2.
• Next, find the exponent button, sometimes labeled \( \text{EXP} \), \( ^ \), or similar. Press this button after entering the base number.
• Then, key in the exponent value. Remember to include the negative sign. So, you would enter -5 after pressing the exponent button.
• Finally, press the equals button \( = \) to get the result.

. Using a calculator, we find that \( (2.2)^{-5} \) approximately equals 0.002915451896.

rounding numbers

Rounding numbers is a crucial skill in math, especially when dealing with long decimal outputs.
To round a number to three decimal places, follow these steps:

• Firstly, locate the fourth decimal place. This is the digit directly after the third decimal place.
• If this digit is 5 or higher, round up the third decimal place by one. If it is lower than 5, keep the third decimal place as it is.
• For our number 0.002915451896, the fourth decimal place is 5. This tells us we need to round 0.00291 up to 0.003.

Rounding makes numbers easier to work with, especially when exact precision isn’t necessary. Remember, always look to the next digit to decide whether to round up or keep the number as is.