exponents and squares numbers and operations. exponents and powers power – the result of raising a...
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Exponents and
SquaresNumbers and Operations
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
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
Guided Practice
• 1. Find 6 squared
• 2. Find 72
• 3. Find 5 cubed
• 4. Find 23
Student Practice• Simplify the following expressions. Write
your answer in expanded and standard notations.
1) 33
2) 23
3) 32
4) 52
5) 210
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
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
Guided Practice
Evaluate each square root.
1.
2.
3.
4
Student Practice
• 1.
• 2.
• 3. 18
• Evaluate each square root. You may use a calculator.
Guided Practice
• 1.
• 2.
• 3.
3√27
3√64
3√343
Student Practice
• 1.
• 2.
• 3.
• Evaluate each cube root. You may use a calculator.
3√512
3√125
3√1331
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
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)
Guided Practice
•(72)(73)
•(32)4
•(23b2c)3
• (32)0
Student Practice• 1. Simplify (53)(54)
• 2. Simplify (42)3
• 3. Simplify (23a4b)2
• 4. Simplify (53b2)0
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
Guided Practice
• 1.
• 2.
Between what two integers does this fall?
Class Practice
• Between what two integers does this fall?
• 1.
• 2.