To solve the expression [tex]\(\left(\frac{2}{3}\right)^{-0.75}\)[/tex], we need to follow these steps:
1. Understanding the Exponent:
- The exponent [tex]\(-0.75\)[/tex] is negative, which means we need to find the reciprocal of the base raised to the positive of that exponent.
2. Rewrite the Expression:
- Rewrite [tex]\(\left(\frac{2}{3}\right)^{-0.75}\)[/tex] as [tex]\(\frac{1} {\left(\frac{2}{3}\right)^{0.75}}\)[/tex].
3. Evaluate the Positive Exponent:
- Calculate [tex]\(\left(\frac{2}{3}\right)^{0.75}\)[/tex]. This step involves raising the fraction [tex]\(\frac{2}{3}\)[/tex] to the power of [tex]\(0.75\)[/tex].
4. Reciprocal of the Result:
- Once you have [tex]\(\left(\frac{2}{3}\right)^{0.75}\)[/tex], take the reciprocal of this value to account for the negative exponent.
Following these steps, the evaluation yields the result:
[tex]\[
\left(\frac{2}{3}\right)^{-0.75} \approx 1.3554030054147672
\][/tex]
So, [tex]\(\left(\frac{2}{3}\right)^{-0.75}\)[/tex] approximately equals [tex]\(1.3554030054147672\)[/tex].
