rules of exponents

Question

use the rules of exponents to simplify the following:

 

1 - x2 times x5 times x10 times x31 =

 

2 - (x2)(third power) times (x4) (second power) =

 

3 - (XY) (2nd power) times (YZ) (3rd power) =

 

 

Answer 1

The rule for exponents that you need to remember cortnee is that whenever you multiply exponents that have the same base all we need to do is sum them up.

 

For problem #1

 

1) x^2 * x^5 * x^31

 

= x^(2+5+31)

 

= x^38

 

 

2) This problem requires us to multiply the powers together and then add them up

 

(x^2) ^3 * (x^4)^2

 

= x^ 6 *  x^8

 

= x^ (6+8)

 

= x^14

 

3) X^2Y^2 * Y^3Z^3

 

= X^2 Y^(2+3) Z^3

 

= X^2Y^5Z^3