Simplifying Fractions w/ variables and exponents?

Question

2x(-3)x(5)
_______

3x(2)



( ) = exponent



please explain how to simplify

Answer 1

Are you asking how to get from the first part of the equation that you noted to the second? If so:
2x + x = 3x
-3 + 5 = 2

Simplification is: 3x(5)

Is the explanation what you were looking for?

Answer 2

vlee1225 is correct, although I think that his answer is a little hard to follow.

Let me see if I can make it a little easier to follow.

Your numerator as I read it 2x to the minus 3 power times x to the fifth power.

Since both are in terms of x, to simplify, add the exponents. Add the minus three exponent to the plus five exponent. The exponent that you come up with is 2.

Your numerator is now 2x to the second power or 2x squared.

The denominator is 3x squared.

You have an x squared term in the numerator and the denominator.

Remember any number divided by itself is equal to one. Therefore x squared divided by x squared is equal to one.

Now your numerator becomes 2 times 1 which is equal to 2 and your denominator become 3 times 1 which is equal to 3.

Your final answer is 2 in the numerator and 3 in the denominator or 2/3.

Does that help?


(Edit) I can see that a number of other responders also answered 2/3, which is the correct answer.

Of course what is really important is that you know how to get there. I know that when you are new at this getting to that answer can be a challenge.

Answer 3

2x^(-3)x(5) / 3x(2)
2x^5/ x^3(3x^2)
2x^5/3x^5
2/3

The main issue here is to know x^-3 is 1/x^3.
This is so because when dealing with exponents that have equal bases, x^3/x^5= x^(3-5), or x^-2 . Thats what the rules say. We know x^3/x^5=1/x^2. Therefore, x^-2 and 1/x^2 must mean the same thing.

There is a second way to do this.
2x^(-3)x^5 /3x^2= 2x^(-3+5) /3x^2
=2x^2/3x^2, =2/3
Hope this helps

Answer 4

When consolidating multiple references of the same variable with exponentials in multiplication, you should just be able to add the exponents:

x(-3) times x(5) = x(2)

So, the answer on the numerator (top) would be 2x(2). Since x(2) is on the numerator and denominator (bottom), you can eliminate if from both and the final answer would be 2/3.

Answer 5

2 x^(-3)x^5 / (3 x^2)
= 2 x^5 / { (x^3)3(x^2) }
= (2/3) x^5/ x^5
= 2/3

Answer 6

You can't do anything with (1) except "square it out" (3x^3/4y^5)^2 = 9x^6/16y^10 5x^8y/2x^5y^3 =5x^3/2y^2 5x^-8y/2x^-2y^-3w^-2 = 5x^2y^3w^2/2x^8y = 5y^2w^2/2x^6 The rule is when multiplying/dividing powers of the same variable, add/subtract the exponents and when raising a power to a power, multiply the exponents. A negative power is just a reciprocal, so I inverted problem 3 to make it easier

Answer 7

2x^-3 x^5/ 3x^2
= 2x^2/3x^2
= 2/3
Remember x^m * x^n = x^(m+n)
so 2x^-3 x^5 = 2x^(-3+5) = 2x^2

Answer 8

the answer is 5raise to power (-1)

Answer 9

cant understand ur ques gal.....