To evaluate [tex]\((0.064)^{-1/3}\)[/tex], follow the detailed steps below:
1. Understand the Expression:
[tex]\((0.064)^{-1/3}\)[/tex] represents raising the number [tex]\(0.064\)[/tex] to the power of [tex]\(-1/3\)[/tex].
2. Interpret the Negative Exponent:
A negative exponent indicates taking the reciprocal of the base. Therefore,
[tex]\[
(0.064)^{-1/3} = \frac{1}{(0.064)^{1/3}}
\][/tex]
3. Calculate the Cube Root:
Next, we need to find the cube root of [tex]\(0.064\)[/tex]. The cube root of a number [tex]\(a\)[/tex] is a number [tex]\(b\)[/tex] such that [tex]\(b^3 = a\)[/tex]. For [tex]\(0.064\)[/tex],
[tex]\[
(0.064)^{1/3} = 0.4
\][/tex]
4. Take the Reciprocal:
Now that we have the cube root of [tex]\(0.064\)[/tex], which is [tex]\(0.4\)[/tex], we can proceed to find the reciprocal:
[tex]\[
\frac{1}{0.4} = 2.5
\][/tex]
So, [tex]\((0.064)^{-1/3} = 2.5\)[/tex].
Therefore, the value of [tex]\((0.064)^{-1 / 3}\)[/tex] is [tex]\(2.5\)[/tex].
