Basic Power/ Power of a product

By Jordan, Jack, Noa and Caitlin

What is the Basic Power Rule?

The basic power rule is used when there is two exponents in a expression. One is outside a parenthesis and the other is not. Example: *(2 squared) squared.*

How does this work?

Well in the example *(2 squared)squared* you use the distributive property to multiply the exponents forming the product. Answer: 2 to the power of 4.

we can change this from exponent form to other forms...

2 squared x 2 squared

2 x 2 x 2 x 2

(2 squared ) squared


This rule works because it uses the distributive property to multiply numbers outside the parentheses. The distributive property allows this to work and it is vital to the rule.

What is the power of a product rule?

The power of a product rule is similar to the previous rule. This rule allows you to multiply numbers with exponents and variables with exponents. For example...

(9*to the 5th power* • n*to the third power*)*squared* = 9*to the 10th power* n*to the 6th power*

Notice how the the number, 9, and the variable, n, don’t mix with each other.

How does this rule work

(3 cubed y to the 4th power) squared

Again

  1. One form you can put it in is First Repeated Multiplication Form

    1. 3 cubed•y to the 4th power •3 cubed •y to the 4th power

  2. Another form you can put it in is Second Repeated Multiplication Form (Do this by simplifying the first repeated multiplication form so there are no exponents left)

    1. 3•3•3•3•3•3•y•y•y•y•y•y•y•y

  3. The last form you can put it in is Power of the Form ab (multiply the exponents from inside the parenthesis with the exponent outside the parenthesis)

    1. 3 to the 6th power •y to the 8th power



It works because it uses the distributive property to multiply, move and simplify numbers to fit into different forms. Again the distributive property is vital to this rule.


Note: Notice how the y

exponents do not add to the

number exponents because

they represent different values.