Simplify (2t^–3)^3(0.4r)^2
A.)3.2r2
B.)1.28r^2/t^-6
C.)1.28R^2/t^9
D.)0.8r^2/t^-6
I think it is A.
Thank You.
(2t^-3)^3 = (2/t^3)^3 = 8/t^9
(.4r)^2 = .16r^2
multiply them to get 1.28r^2/t^9
(C)
Thank You.
Well, I hate to break it to you, but option A is not the correct answer! 😅 Let's give it another shot, shall we?
To simplify this expression, let's break it down step-by-step.
First, let's take care of the term (2t^–3)^3. To simplify this, we raise both the coefficient 2 and the variable t to the power of 3. So, we get:
2^3 * t^(-3*3) = 8 * t^(-9) = 8/t^9
Now, let's tackle the second term (0.4r)^2. Similar to before, we raise both the coefficient 0.4 and the variable r to the power of 2:
(0.4)^2 * r^2 = 0.16 * r^2 = 0.16r^2
Now we have (8/t^9) * (0.16r^2). To multiply these together, we simply multiply the coefficients and the variables separately:
(8 * 0.16) * (t^(-9) * r^2) = 1.28 * t^(-9) * r^2
Thus, the correct simplified expression is 1.28 * t^(-9) * r^2. So, the answer is C) 1.28R^2/t^9.
Hope that clears things up! 🤡
To simplify the expression (2t^(-3))^3(0.4r)^2, we can start by simplifying the individual terms.
(2t^(-3))^3 = 2^3 * (t^(-3))^3 = 8 * t^(-9) = 8/t^9
(0.4r)^2 = 0.4^2 * r^2 = 0.16r^2
Now, we can substitute these simplified terms back into the expression:
(2t^(-3))^3(0.4r)^2 = (8/t^9)(0.16r^2) = (8 * 0.16 * r^2) / t^9 = 1.28r^2 / t^9
Therefore, the simplified expression is 1.28r^2/t^9.
Thus, the correct answer is C.) 1.28R^2/t^9.
To simplify the expression (2t^–3)^3(0.4r)^2, we need to use the exponent rules and simplify each term.
First, let's simplify (2t^–3)^3:
When raising a power to another power, you multiply the exponents. So, (2t^–3)^3 = 2^3 * (t^–3)^3.
2^3 = 8.
And for (t^–3)^3, we multiply the exponents again: t^–3 * t^–3 * t^–3 = t^–9.
So, (2t^–3)^3 simplifies to 8t^–9.
Next, let's simplify (0.4r)^2:
When raising a product to a power, you raise each factor to that power. So, (0.4r)^2 = 0.4^2 * r^2.
0.4^2 = 0.16.
Therefore, (0.4r)^2 simplifies to 0.16r^2.
Now, let's substitute the simplified forms back into the original expression:
(2t^–3)^3(0.4r)^2 = (8t^–9)(0.16r^2).
Now, let's simplify the expression further by applying the multiplication rule for exponents:
8t^–9 * 0.16r^2 = 1.28t^–9r^2.
Therefore, the simplified expression is 1.28t^–9r^2.
So, the correct answer is option C.) 1.28R^2/t^9.