^{ }
Basics
Number^{Power}
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 = 7^{4} = 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 = -7^{4} = -2401
7 to the power of -4 = 7^{-4} = × × × = 0.000416493
Number^{A} × Number^{B }= Number^{A+B}
7^{4} × 7^{5} = 7^{4+5} = 7^{9}
is the power command.
It is possible that questions involving powers will be in the calculator-prohibited section of the test.
Question
What is 9^{6}?
Answer
531441
Calculator Click | What You See | Comment |
blinker | clears screen | |
9 6 | 9^{6} | 9 to the power of 6 |
531441 | Answer | |
Power |
Question
According to the calculator, what is the value of -9^{6}?
According to the calculator, what is the value of (-9)^{6}?
Observe how parentheses change the results of these calculations.
Answer
-9^{6} = -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 |
blinker | clears screen | |
9 6 | -9^{6} | |
-531441 | ||
blinker | clears screen | |
9 6 | (-9)^{6} |
Parentheses protect order of operations. |
531441 | ||
Power |
Question
What is 9^{-6}?
Answer
0.000001882
Calculator Click | What You See | Comment |
blinker | clears screen | |
9 -6 | 9^{-6} | 9 to the power of -6 |
0.000001882 | Answer | |
Power |
Question
Without using the calculator, what is 8^{4} × 8^{6 }? Give your answer in exponent form.
Answer
8^{10}
Answer Process
Number^{A} × Number^{B }= Number^{A+B}
8^{4} × 8^{6} = 8^{4+6} = 8^{10}
Question
Without using the calculator, what is ? Give your answer in exponent form.
Answer
Answer Process
Practice – Questions
1. What is 6^{4}?
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 -6^{4}?
6. What is 6^{-4}?
7. Without using the calculator, what is 3^{7} × 3^{8 }? Give your answer in exponent form.
8. Without using the calculator, what is 3^{7} × 3^{-3 }? Give your answer in exponent form.
9. Without using the calculator, what is ? Give your answer in exponent form.
10. Without using the calculator, what is ? Give your answer in exponent form.
Practice – Answers
1. 1296
2. 1296
3. 1296
4. 1296
5. -1296
6. 0.000771605
7. 3^{15}
8. 3^{4}
9. 5^{4}
10. 5^{-8}