In Lesson 3, we will explore the properties of exponents when it comes to multiplication.
Recall that an exponent is a shorthand way of writing the repeated multiplication of a base number. For example, 2³ means 2 multiplied by itself three times: 2 x 2 x 2 = 8.
When we multiply two numbers with exponents, we can use the following rules:
Product Rule: When multiplying two numbers with the same base, we can add their exponents.
For example:
2² x 2³ = 2^(2+3) = 2^5 = 32
This means that 2² x 2³ is the same as 2 to the power of 5.
Quotient Rule: When dividing two numbers with the same base, we can subtract their exponents.
For example:
4⁵ / 4³ = 4^(5-3) = 4² = 16
This means that 4⁵ divided by 4³ is the same as 4 to the power of 2.
Power Rule: When raising a number with an exponent to another exponent, we can multiply the exponents.
For example:
(2⁴)³ = 2^(4x3) = 2¹² = 4096
This means that (2⁴)³ is the same as 2 to the power of 12.
These rules can also be applied to variables with exponents. For instance, when multiplying two variables with the same base, we can add their exponents.
If we have x² times x³, we can add the exponents to get x^(2+3) = x^5.
Similarly, when dividing two variables with the same base, we can subtract their exponents.
If we have y^7 divided by y^4, we can subtract the exponents to get y^(7-4) = y^3.
When raising a variable with an exponent to another exponent, we can multiply the exponents.
If we have (z^2)^3, we can multiply the exponents to get z^(2x3) = z^6.
By understanding these rules, we can simplify expressions with exponents and make calculations easier and quicker.
UNIT 5
Polynomials and Properties of Exponents
LESSON 3
Exponents and Multiplication
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