How to rewrite an expression with negative exponents such as :
-12(3x-1)^-5 *(6x+7)^5 + 30(3x-1)^-4 *(6x+7)^4
common factor is 6 but what can I pull out from the (3x-1)^-5 and (3x-1)^-4 ?
( 3 x - 1 ) ^ -5 = 1 / ( 3 x -1 ) ^ 5
( 3x - 1 ) ^ - 4 = 1 / ( 3 x -1 ) ^ 4
- 12 ( 3 x -1 ) ^ - 5 * ( 6 x + 7 ) ^ 5 + 30 ( 3 x - 1 ) ^ - 4 * ( 6 x + 7) ^ 4 =
[ - 12 ( 6 x + 7 ) ^ 5 ) + 30 * ( 3 x - 1 ) * ( 6 x + 7 ) ^ 4 ] / ( 3 x - 1 ) ^ 5 =
6 * ( 6 x + 7 ) ^ 4 * [ ( - 2 ) * ( 6 x + 7 ) + 5 * ( 3 x - 1 ) ] / ( 3 x - 1 ) ^ 5 =
6 * ( 6 x + 7 ) ^ 4 * ( - 12 x - 14 + 15 x - 5 ) / ( 3 x - 1 ) ^ 5 =
6 * ( 6 x + 7 ) ^ 4 * ( 3 x - 19 ) / ( 3 x - 1 ) ^ 5
To rewrite the expression with negative exponents, you need to understand the properties of exponents and how to manipulate them.
Let's start with the expression:
-12(3x-1)^-5 *(6x+7)^5 + 30(3x-1)^-4 *(6x+7)^4
To simplify it, you can rewrite the negative exponents by flipping the terms to the numerator instead of the denominator. Here's how you can do it step by step:
Step 1: Rewrite the negative exponents by flipping the terms:
-12/(3x-1)^5 *(6x+7)^5 + 30/(3x-1)^4 *(6x+7)^4
Step 2: Identify the common factors:
From the term (3x-1)^-5 and (3x-1)^-4, the common factor that can be pulled out is (3x-1)^-4.
Step 3: Pull out the common factor:
-12/(3x-1)^4 * (3x-1) *(6x+7)^5 + 30/(3x-1)^4 * (6x+7)^4
Step 4: Simplify the expression:
-12(6x+7)^5/(3x-1) + 30(6x+7)^4/(3x-1)
That's it! You have successfully rewritten the expression with negative exponents by pulling out the common factor.