Question

simplify (2t^-3)^3(0.4r)^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

Using the rules of exponents, we can simplify the expression.

(2t^-3)^3(0.4r)^2

First, let's simplify (2t^-3)^3:
(2t^-3)^3 = 2^3 * (t^-3)^3 = 8 * t^-9 = 8/t^9

Now let's simplify (0.4r)^2:
(0.4r)^2 = 0.4^2 * r^2 = 0.16 * r^2

Finally, putting it all together:
(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.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression (2t^-3)^3 * (0.4r)^2, let's break it down step by step:

Step 1: Simplify the exponents within each term.
(2t^-3)^3 can be rewritten as (2^3)(t^-3)^3 and (0.4r)^2 remains the same.

Step 2: Simplify the exponents.
(2^3)(t^-3)^3 simplifies to 8t^-9. (t^-3)^3 can be simplified as t^-9 because we multiply the exponents: -3 * 3 = -9.
(0.4r)^2 remains the same.

Step 3: Combine the terms.
Now we have 8t^-9 * (0.4r)^2. Since (0.4r)^2 simplifies to 0.16r^2, we can rewrite it as 8t^-9 * 0.16r^2.

Therefore, the simplified expression is 8t^-9 * 0.16r^2, or written in a different form: 0.16r^2 * 8t^-9.