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

Answer 1

To simplify this expression, we need to apply the exponent rules.

First, let's simplify the exponent of t.
t^-3 means 1/t^3.

So (2t^-3)^3 becomes (2(1/t^3))^3.

To simplify further, we can apply the power rule for exponents, which states that (a^m)^n = a^(m*n).

Applying this rule, we have:
(2(1/t^3))^3 = 2^3 * (1/t^3)^3.

Simplifying, we get:
8 * 1^3/t^(3*3) = 8/t^9.

Now let's incorporate the second part of the expression, 0.4r.

Multiplying (8/t^9) by 0.4r gives us:
(8/t^9)(0.4r) = (8 * 0.4 * r) / t^9 = (3.2r) / t^9.

Therefore, the simplified expression is 3.2r / t^9.