We had a substitute in math on friday and we got a worksheet, but he didn't explain how to do it very well. Could someone work out a problem for me?
1. (2b^3)^3 * 3(b^-4)^2 =
I have no clue how to do this. The answer key says it is 24b^2 but I can't get that
Oh wait, the answer is just 24b. I wrote the wrong answer. But I can't get that either.
(2b^3)^3 * 3(b^-4)^2
step #1) = 8b^9 * 3b^-8
step #2) = 24b
Explanation:
step 1: (2^3 is 8, b^3^3 = b^9, b^-4^2 = b^-8)
step 2: Multiply the coefficients (8*3=24). Muliply the b terms: b^9 * b^-8 = b^1 = b
Sure! Let's break down the problem step by step.
Step 1: Simplify the bases inside the parentheses.
- In the first set of parentheses, we have "2b^3." To simplify this, we raise each term inside the parentheses to the power of 3: (2b^3)^3 = 2^3 * (b^3)^3 = 8 * b^9.
- In the second set of parentheses, we have "b^-4." To simplify this, we bring the term with a negative exponent to the denominator: (b^-4)^2 = (1/b^4)^2 = 1^2 / (b^4)^2 = 1/b^8.
Step 2: Combine the simplified expressions.
Now that we have simplified both sets of parentheses, we can multiply them together: (2b^3)^3 * 3(b^-4)^2 = (8b^9) * (3 * (1/b^8)).
Step 3: Simplify the product of the expressions.
To simplify the product, we multiply the numbers and combine the variables:
- Multiply the numbers: 8 * 3 = 24.
- Combine the variables: b^9 * (1/b^8) = b^(9-8) = b^1 = b.
So the simplified expression is 24b.