Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a...
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![Page 1: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/1.jpg)
Exponents and
SquaresNumbers and Operations
![Page 2: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/2.jpg)
Exponents and Powers
• Power – the result of raising a base to an exponent. Ex. 32
• Base – the number being raised to the exponent. Ex. 32
3 is the base
• Exponent – the number the base is being raised to. Ex. 32
2 is the exponent
![Page 3: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/3.jpg)
Squares and Cubes
3
3The area of the square is 3 x 3, or 32 , or 3 squared
3
33
The area of the cube is 3 x 3 x 3 or 33 , or 3 cubed
![Page 4: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/4.jpg)
Guided Practice
• 1. Find 6 squared
• 2. Find 72
• 3. Find 5 cubed
• 4. Find 23
![Page 5: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/5.jpg)
Student Practice• Simplify the following expressions. Write
your answer in expanded and standard notations.
1) 33
2) 23
3) 32
4) 52
5) 210
![Page 6: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/6.jpg)
Square Roots
• Square root – a number which multiplied by itself, gives you the original number. Example: 4 × 4 = 16, so the square root of 16 is 4.
• Perfect square – a number whose square root is a whole number. Example 9 = 3 x 3
![Page 7: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/7.jpg)
Square Roots
Square root symbol
Number that I want the square root of
Square root symbol (Radical Symbol)- the symbol used to denote square root.
Example: √9 = 3
3Cube root
symbol
Number that I want the cube root of
Example: 3√8 = 2
![Page 8: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/8.jpg)
Guided Practice
Evaluate each square root.
1.
2.
3.
4
![Page 9: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/9.jpg)
Student Practice
• 1.
• 2.
• 3. 18
• Evaluate each square root. You may use a calculator.
![Page 10: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/10.jpg)
Guided Practice
• 1.
• 2.
• 3.
3√27
3√64
3√343
![Page 11: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/11.jpg)
Student Practice
• 1.
• 2.
• 3.
• Evaluate each cube root. You may use a calculator.
3√512
3√125
3√1331
![Page 12: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/12.jpg)
Rules of Exponents
• 1. When you multiply two terms with the same base, you ADD the exponents.
• 2. When you have an exponent expression that is raised to a power, you can multiply the exponent and power:
• 3. When you have anything to the power zero it is just "1"
( x m ) ( x n ) = x( m + n )
( xm ) n = x m n
x0 = 1
![Page 13: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/13.jpg)
Exponents and Grouping Symbols
• To evaluate powers involving grouping symbols:
• (ab)2 = (ab)(ab) = a x a x b x b = a2b2
• The power is applied to each value within the parenthesis.
• (This applies only when there is one term in parenthesis raised to a power)
![Page 14: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/14.jpg)
Guided Practice
•(72)(73)
•(32)4
•(23b2c)3
• (32)0
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Student Practice• 1. Simplify (53)(54)
• 2. Simplify (42)3
• 3. Simplify (23a4b)2
• 4. Simplify (53b2)0
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Working with Squares
• Between what two integers does the following fall? :
√5 √4 √9 2 3
Answer: √5 lies between 2 and 3
Ex: √5
1. Identify two closest square roots
2. Evaluate square roots
![Page 17: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/17.jpg)
Guided Practice
• 1.
• 2.
Between what two integers does this fall?
![Page 18: Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649ead5503460f94bb3ac7/html5/thumbnails/18.jpg)
Class Practice
• Between what two integers does this fall?
• 1.
• 2.