Raising a number to a power is a quick way to multiply a number by itself. For example, 25, which you read as two to the fifth power, means that you multiply 2 by itself 5 times:
25 = 2 x 2 x 2 x 2 x 2 = 32
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- The left-hand side, negative 1 over 6 times negative 6. Well that just equals 1. So we just get x is equal to 5 times negative 1/6. Well, that's negative 5/6. And if you wanted to check it, you could just take that x equals negative 5/6 and put it back in the original question to confirm that it worked.
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The number 2 is called the base, and the number 5 is called the exponent.
Powers of ten — that is, powers with 10 in the base — are especially important because the number system is based on them. Fortunately, they’re very easy to work with. To raise 10 to the power of any positive whole number, write down the number 1 followed by the number of 0s indicated by the exponent. For example, 103 is 1,000.
Here are some important rules for finding powers that contain 0 or 1:
- Every number raised to the power of 1 equals that number itself.
- Every number (except 0) raised to the power of 0 is equal to 1. For example, 100 is 1 followed by no 0s — that is, 1.
- The number 0 raised to the power of any number (except 0) equals 0, because no matter how many times you multiply 0 by itself, the result is 0.Mathematicians have chosen to leave 00 undefined — that is, it doesn’t equal any number.
- The number 1 raised to the power of any number equals 1, because no matter how many times you multiply 1 by itself, the result is 1.
When you multiply any number by itself, the result is a square number. So, when you raise any number to the power of 2, you’re squaring that number. For example, here’s 52, or five squared:
52 = 5 x 5 = 25
The inverse of squaring a number is called finding the square root of a number (inverse operations undo each other. When you find the square root of a number, you discover a new number which, when multiplied by itself, equals the number you started with. For example, here’s the square root of 25:
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Sample questions
- Noteplan 1 6 18 download free. What is 34?81. The expression 34 tells you to multiply 3 by itself 4 times:3 x 3 x 3 x 3 = 81
- What is 106?1,000,000. Using the power of ten rule, 106 is 1 followed by six 0s, so 106 = 1,000,000.
- What is the following?6. You want to find a number that, when multiplied by itself, equals 36. You know that 6 x 6 = 36, so
- What is the following?16. You want to find a number that, when multiplied by itself, equals 256. Try guessing to narrow down the possibilities. Start by guessing 10:10 x 10 = 100256 > 100, so the answer is greater than 10. Guess 20:20 x 20 = 400256 < 400, so the answer is between 10 and 20. Guess 15:15 x 15 = 225256 > 225, so the answer is between 15 and 20. Guess 16:16 x 16 = 256This is correct, so
Practice questions
- Find the value of the following powers:a. 62b. 35c. 27d. 28 (Hint: You can make your work easier by using the answer to c.)
- Find the value of the following powers:a. 104b. 1010c. 1015d. 101
Following are the answers to the practice questions:
- Find the value of the following powers:a. 62 = 6 x 6 = 36.b. 35 = 3 x 3 x 3 x 3 x 3 = 243.c. 27 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128.d. 28 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256. You already know from part c that 27 = 128, so multiply this number by 2 to get your answer: 128 x 2 = 256.
- Find the value of the following powers:a. 104 = 10,000. Write 1 followed by four 0s.b. 1010 = 10,000,000,000. Write 1 followed by ten 0s.c. 1015 = 1,000,000,000,000,000. Write 1 followed by fifteen 0s.d. 101 = 10. Any number raised to the power of 1 is that number.
Related Pages
Place Value Chart
Lesson Plans And Worksheets For Grade 4
More Lessons For Grade 4
Place Value Chart
Lesson Plans And Worksheets For Grade 4
More Lessons For Grade 4
New York State Common Core Math Grade 4, Module 1, Lesson 2
The following diagrams show how to multiply and divide by 10 using the place value chart. Scroll down the page for examples and solutions.
NYS Math Grade 4, Module 1, Lesson 2 Concept Development
Problem 1:
Multiply single units by 10 to build the place value chart to 1 million. Divide to reverse the process.
Multiply single units by 10 to build the place value chart to 1 million. Divide to reverse the process.
- 10 × 1 one is 1 ten
- 10 × 1 ten is 1 hundred
- 10 × 1 hundred is 1 thousand
- 10 × 1 thousand is 1 ten thousand
- 10 × 1 ten thousand is 1 hundred thousand
- 10 × 1 hundred thousand is 1 million
Problem 2:
Multiply multiple copies of one unit by 10
(e.g., 10 × 4 ten thousands).
Multiply multiple copies of one unit by 10
(e.g., 10 × 4 ten thousands).
- Draw number disks and write a multiplication sentence to show the value of 10 times 4 ten thousands.
- 10 times 4 ten thousands = 40 ten thousands = 4 hundred thousands.
- Explain how you know this equation is true.
10 × 4 ten thousands = 40 ten thousands = 4 hundred thousands.
Place Value Chart And Multiply By 10
After having built the place value chart by multiplying by ten, quickly review the process simply moving from right to left on the place value chart, and then reversing and moving left to right.
Move right when multiply by ten and move left to divide by ten.
(e.g. 2 tens times 10 equals 2 hundreds times 10 equals 2 thousands divided by 10 equals 2 hundreds divided by 10 equals 2 tens.)
(e.g. 2 tens times 10 equals 2 hundreds times 10 equals 2 thousands divided by 10 equals 2 hundreds divided by 10 equals 2 tens.)
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Problem 3:
Divide multiple copies of one unit by 10:
2 thousands ÷ 10.
Solve in unit form:
2 thousands ÷ 10
Divide multiple copies of one unit by 10:
2 thousands ÷ 10.
Solve in unit form:
2 thousands ÷ 10
Divide Multiple Copies Of One Unit By 10
Solve in unit form: 4 thousands ÷ 10
- Use a place value chart. Represent 4 thousands on a place value chart and then change for smaller units so we can divide.
- Change each thousand for 10 smaller units. 4 thousands can be changed to be 40 hundreds because 4 thousands and 40 hundreds are equal.
- 4 thousands ÷ 10 is 4 hundreds because 4 thousands unbundled becomes 40 hundreds.
40 hundreds divided by 10 is 4 hundreds. - 4 thousands ÷ 10 = 40 hundreds ÷ 10 = 4 hundreds
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Problem 4:
Multiply and divide multiple copies of two different units by 10.
Multiply and divide multiple copies of two different units by 10.
NYS Common Core Math Module 1, Grade 4, Lesson 2 Problem Set
- As you did during the lesson, label and represent the product or quotient drawing disks on the place value chart.
a. 10 × 2 thousands = _____ thousands = _____
c. 4 thousands ÷ 10 = _____ hundreds ÷ 10 = ______
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- Fill in the blanks to complete each number sentence. Respond first in unit form, then in standard form.
- Fill in the blanks to complete each number sentence. Respond first in unit form, then in standard form.
- Jacob saved 2 thousand dollar bills, 4 hundred dollar bills, and 6 ten dollar bills to buy a car. The car costs 10 times as much as he has saved. How much does the car cost?
- Show Video Lesson
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NYS Common Core Math Module 1, Grade 4, Lesson 2 Homework
- As you did during the lesson, label and represent the product or quotient drawing disks on the place value chart.
a. 10 × 4 thousands = ____ thousands = ____
b. 4 thousands ÷ 10 = ____ hundreds ÷ 10 = _____ - Fill in the blanks to complete each number sentence. Respond first in unit form, then in standard form.
- Fill in the blanks to complete each number sentence. Respond first in unit form, then in standard form.
- Emily collected $950 selling Girl Scout cookies all day Saturday. Emily’s troop collected 10 times as much as she did. How much money did Emily’s troop raise?
- On Saturday, Emily made 10 times as much as on Monday. How much money did Emily collect on Monday?
- Show Video Lesson
Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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