In Algebra how do you multiply two letters when they have a little number with them (to the power to)?

Question

I know that if you have x to the power of two + x to the power of 3 it would be x to the power of 5. If it was x to the power of 2 x x to the power of 5 would it be 2x to the power of ten?

Answer 1

The caret symbol (^) is used to write exponents. So x to the power of two + x to the power of 3 is written as x^2 + x^3. This is not equal to x^5. You can't combine them if they have different exponents. When you multiply them, you add exponents. for instance: x^2 * x^3 = x^5.

Answer 2

Sorry Power gets added during Multipication not in addition SO you are wrong when you say " I know that if you have x to the power of two + x to the power of 3 it would be x to the power of 5. "
Rather you shoud say " I know that if you have x to the power of two * x to the power of 3 it would be x to the power of 5."
You can only add if the power are same like x^4 + 2x^4 = 3x^4

Similarly x to the power of 2 x x to the power of 5 would it be x to the power of seven.

I hope you understand.

Answer 3

You cannot add variables with different exponents. I.e., x^2 + x^ 3 cannot be added. You could factor it to get x^2(1+x), but that's about it. For x^2 times x^5, the answer would be x^7 - you add the exponents. However, for x^2 raised to the 5th power, (x^2)^5, you multiply the exponents to get x^10.

Answer 4

x to the power of 10

Answer 5

well, first of all, x^2+x^3 doesn't =x^5. the 2nd thing is that x^2*x^5=x^7. there are a few ways u can tke this problem. one way is, expand the exponents. x^2*x^5=x*x*x*x*x*x*x=x^7. u can also solve this problem by inputting a value for x. lets say its 2. 2^2*2^5=4x32=128, which is = to 2^7. also, keep in mind that when u r adding, u cannot do it without knowing the actual value of x. the best u can do in the first problem is simplify it to:
(x^2)(x+1), but it can no longer be simplified.

Answer 6

Simple rule: must be the same numbers, then add the powers to multiply.
So
x^2 . x^3 = x^5, and
x^2 . x^5 = x^7
But x^2 . y^3 cannot be simplified (because different quantities raised to the powers).

However if you have say (2x)^3 you can separate it out,
thus: (2^3) .( x^3) = 8 x^3

Answer 7

when multiplying letters with powers, first make sure they are the same letter, because if not it wont work.
When multiplying, you add the powers together, being careful if there are negative powers.
When dividing, subtract the second power from the first, going into negatives if necessary.
Hope this is helpful if you come across any similar questions!!

Answer 8

i think your question is x^2 times x^5?

then you'd get x^7

you have to add the powers together, 2+5 in this case, to get 7

Answer 9

See this site for exponent rules

http://www.purplemath.com/modules/exponent.htm

Answer 10

James P is correct.