Simplify make sure the answer has no negative exponents.

Question

9x^-1u⁶v^-8 *2xv⁶ *2u³ 

 

 

Can someone please explain how to find the answer in a simple form?

Answer 1

Hi Berenice!!

 

When simplifying expressions such as these, I like to save the negative exponents until the very end. So first we need to combine these terms into one term. Remember, when you multiply variables together, you add the exponents and when you divide the variables you subtract (make sure you do numerator exponent - denominator exponent; doesn't matter which number is bigger).

 

So for this problem, we are multiplying all the terms together so we will combine each like variable together and add their exponents:

 

(9 * 2 * 2)(x ^ {-1 + 1})(u ^ {6 + 3})(v ^ {-8 + 6})

36 x^0 u^9 v^-2

 

Now that we have one term, we can now address the negative exponents. Remember, the rule for negative exponent is to write the reciprocal. Once you do that, it changes the exponent to be a positive. So x^-a = 1/(x^a). Also, 1/(x^-a) = x^a

 

The only variable that has a negative exponent is v. So that is the ONLY one you write the reciprocal of. Everything else stays as is.

 

(36 u^9)/(v^2) {Remember x^0 = 1; anything to the 0 power always equals 1)

 

Hope this helps!