Power

power

Basics
NumberPower

The term power refers to how many times a number is multiplied by itself.

A power is also known as an exponent.

7 to the power of 2 = 7² = 7 × 7 = 49
7 to the power of 2 is also known as 7 squared.

7 to the power of 3 = 7³ = 7 × 7 × 7 = 343
7 to the power of 3 is also known as 7 cubed.

7 to the power of 4 = 74 = 7 × 7 × 7 × 7 = 2401

In order to get the correct answer when calculating the power of a negative number,
place the negative number in parentheses to protect the order of operations.
Right:  -7 to the power of 4 = (-7)4 = 2401
Wrong:  -7 to the power of 4 = -74 = -2401

7 to the power of -4 = 7-4 = \bf\displaystyle\frac{1}{7} × \bf\displaystyle\frac{1}{7} × \bf\displaystyle\frac{1}{7} × \bf\displaystyle\frac{1}{7} = 0.000416493

NumberA × Number= NumberA+B
74 × 75 = 74+5 = 79

\bf\displaystyle\frac{\text{Numbe}{{\text{r}}^{\text{A}}}}{\text{Numbe}{{\text{r}}^{\text{B}}}}\text{= Numbe}{{\text{r}}^{\text{A-B}}}
\bf\displaystyle\frac{{{7}^{11}}}{{{7}^{3}}}={{7}^{11-3}}={{7}^{8}}

power  is the power command.

It is possible that questions involving powers will be in the calculator-prohibited section of the test.


Question

What is 96?

Answer
531441

Calculator Click What You See Comment
clear blinker clears screen
power 6 96 9 to the power of 6
enter 531441 Answer
Power


Question
According to the calculator, what is the value of -96?
According to the calculator, what is the value of (-9)6
?
Observe how parentheses change the results of these calculations.

Answer
-96 = -531441
(-9)6 = 531441

Answer Process
The second calculation illustrates the way parentheses protect the order of operations when working with the power of a negative number.

Calculator Click What You See Comment
clear blinker clears screen
(-) 9 power 6 -96
enter -531441
clear blinker clears screen
( (-) 9 ) power 6 (-9)6
Parentheses protect order of operations.
enter 531441
Power


Question

What is 9-6?

Answer
0.000001882

Calculator Click What You See Comment
clear blinker clears screen
power -6 9-6 9 to the power of -6
enter 0.000001882 Answer
Power


Question
Without using the calculator, what is 84 × 8?  Give your answer in exponent form.

Answer
810

Answer Process
NumberA × Number= NumberA+B
84 × 86 = 84+6 = 810


Question
Without using the calculator, what is \bf\displaystyle\frac{{{4}^{10}}}{{{4}^{3}}} ?  Give your answer in exponent form.

Answer
\bf\displaystyle{{4}^{7}}

Answer Process
\bf\displaystyle\frac{\text{Numbe}{{\text{r}}^{\text{A}}}}{\text{Numbe}{{\text{r}}^{\text{B}}}}\text{= Numbe}{{\text{r}}^{\text{A-B}}}
\bf\displaystyle\frac{{{4}^{10}}}{{{4}^{3}}}={{4}^{10-3}}={{4}^{7}}


Practice – Questions
1.  What is 64?

2.  What is 6 to the power of 4?

3.  What is (-6)4?

4.  What is -6 to the power of 4?

5.  What is -64?

6.  What is 6-4?

7.  Without using the calculator, what is 37 × 3?  Give your answer in exponent form.

8.  Without using the calculator, what is 37 × 3-3 ?  Give your answer in exponent form.

9. Without using the calculator, what is \bf\displaystyle\frac{{{5}^{12}}}{{{5}^{8}}} ?  Give your answer in exponent form.

10. Without using the calculator, what is \bf\displaystyle\frac{{{5}^{12}}}{{{5}^{20}}} ?  Give your answer in exponent form.


Practice – Answers

1.  1296

2.  1296

3.  1296

4.  1296

5.  -1296

6.  0.000771605

7.  315

8.  34

9.  54

10.  5-8

About Scott Solomon

HowtoPasstheGED.com gears up adult learners for the recently redesigned, newly computerized GED. ScottSolomon.com delves into my literary fiction.
This entry was posted in (2) Crunching, (III) Mathematical Reasoning and tagged , , , , , , , , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s