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

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