Exponents? 8 questions?

Question

1. (2x)^5 / (2x)^5

2.(x^3)^3

3.(-3y^2)^3

4.(3x^2)(-2x^5)^3

5.(2x^3y^-2)^3

6.(2x)^2(-3x)^4

7.espress using a positive exponent .... 5^-3

8. express using a negative exponent..... 1/y^8

Answer 1

Do your own Homework.

Answer 2

The first one is simple.  Anything divided by itself is 1.

2.  (x^3 * x^3 * x^3) - you add the exponents so the answer is x^9

3.  (-3y^2)^3 is (-3y^2)(-3y^2)(-3y^2).  Use the FOIL method to multiply this by multiplying the first two terms and then multiplying the result by the third term.  Thus... (-3y^2)(-3y^2) - 9y^4 and then -9y^4(-3y^2) is 27y^6.  (Watch your signs!  That's where I go wrong most of the time.  A negative times a negative is a positive and a negative times a positive is a negative.  If you accidentally drop a sign, the answer is wrong even if the numbers are right.

4.  In number four, you need to use the Order of Operations to solve it properly.  Remember PEMDAS - Parenthenses, Exponents, Multiply, Divide, Add, Subtract.  I learned it by a sentence instead of PEMDAS - Please Excuse My Dear Aunt Sally.  But it's a very important thing to remember ALWAYS.

So... (3x^2)(-2x^5)^3 means that since there is nothing we can do inside either of the parenthesis terms, we need to deal with the outside exponent, ^3 first.  So (-2x^5)^3 is -2x^8.  Then multiply that times the first term, 3x^2.  Thus, (3x^2)(-2x^8) or -6x^10.

Keep following this method through number 6.

For numbers 7 and 8, just remember this:  when you have a negative exponent, its inverse is also true.  In other words, 5^-3 is the same as 1/5^3.  Understand?  Write it out so you can really see it.  This is a hard way to write equations.

For number 8 it is the opposite.  1/y^8 is the same as y^-8.

Hope this helps.

The two links I put down here can answer a lot of math questions for you.

:)

Answer 3

I will first give you a word of warning that these are easy concepts and you need to be paying attention in class. To get your ball rolling with the last two remember:

when the exponent is negative in the numerator it can also be shown as positive in the denominator.

ie     2^-7 = 1/(2^7)

Now pay attention to your teacher!

Answer 4

1.any number / the number itself =...........

2. X^9

3. 729  Y^6

4.the question's not clear ...the answer is either -24X^17 or 216X^125

5.8X^9Y^8

6.324X^6

7.1/5^3

8.y^ -8

but srsly.........DO YOUR OWN HW!!!!!!!