PROPERTIES OF
EXPONENTS
SQUARE ROOTS
8THº
Math
TEACHER ANDREA BARRIA
POWERS OF EXPONENTS
The power (or exponent) of a number says how many times to use the number in a multiplication.
It is written as a small number to the right and above the base number.
In 82 the "2" says to use 8 twice in a multiplication,
so 82 = 8 × 8 = 64
• In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"
1. Example: 24 = 2 × 2 × 2 × 2 = 16
the power is 4: "2 to the power 4 is 16"
or we can say the power is the result of 16: "the 4th power of 2 is 16
2. Example: 53 = 5 × 5 × 5 = 125
In words: 53 could be called "5 to the third power", "5 to t
or simply "5 cubed"
he power 3"
MULTIPLICATION
• 1. Product
of Powers
Examples
1. Since the Powers have the same base,
keep the base and add the exponents.
2. Group powerswith the same base
together.
3. Add the exponents of power with the
same base.
1. Group Powers with the same base
together.
2. Add the exponentsof Powers with
the same base.
3. Group the positive exponents and
add sincethey have the same base
4. Add the like bases.
MULTIPLICATION
• 2. power of a product
• Each base raise to the same exponent
Examples
MULTIPLICATION
• 3. Power of a power property
1. Use the power of a
power property
2. Multiply the exponents
Zero multiplied by any number
is zero.
Any number raised to the zero
is 1
Examples
1. Use the power of a power
property
2. Simplify the exponent of the
first term.
3. Use the product of a power
property with the same base
4. Write with a positive exponent
1. Use the power of a power
property
2. Simplify each term
3. Add the exponents
PROBLEM SOLVING
PROBLEM SOLVING
DIVISION
Examples
DIVISION
Examples
Use the power property and simplify
Examples
Use the power of a product property
Use the power of a quotient and simplify
Examples
NEGATIVE POWER
Examples
1. Change or rewrite the
expresión with a positive
exponent
2. Use the Powers of a quotient
property
Examples
SQUARE ROOT
• Roots" (or "radicals") are the "opposite" operation of applying exponents; we can "undo" a
power with a radical, and we can "undo" a radical with a power. For instance, if we square 2,
we get 4, and if we "take the square root of 4", we get 2; if we square 3, we get 9, and if we
"take the square root of 9", we get 3.
Any number raised to the power of 2 can be modeled using a
polygon--the square! That's why we call raising a number to the
second power "squaring the number." The perfect squares are
squares of whole numbers. Here are the first five perfect squares.
Examples
Examples
Find out how the answer was obtained