Sure! Let's break it down step-by-step to solve the expression [tex]\((25)^{-\frac{1}{3}} \times \sqrt[3]{16}\)[/tex].
1. Evaluate [tex]\((25)^{-\frac{1}{3}}\)[/tex]:
- The expression [tex]\((25)^{-\frac{1}{3}}\)[/tex] stands for the cube root of the reciprocal of 25.
- First, find the cube root of 25, which is [tex]\( \sqrt[3]{25} \)[/tex].
- The numerical value of the cube root of 25 is approximately [tex]\( \sqrt[3]{25} \approx 2.924017738212866 \)[/tex].
- Taking the reciprocal of this value, we get [tex]\( (25)^{-\frac{1}{3}} \approx 0.3419951893353394 \)[/tex].
2. Evaluate [tex]\(\sqrt[3]{16}\)[/tex]:
- The cube root of 16 is denoted as [tex]\( \sqrt[3]{16} \)[/tex].
- The numerical value of the cube root of 16 is approximately [tex]\( \sqrt[3]{16} \approx 2.5198420997897464 \)[/tex].
3. Multiply both values:
- Now, multiply [tex]\((25)^{-\frac{1}{3}}\)[/tex] and [tex]\(\sqrt[3]{16}\)[/tex].
- That is, [tex]\( 0.3419951893353394 \times 2.5198420997897464 \)[/tex].
4. Final result:
- By performing the multiplication, we get [tex]\( 0.3419951893353394 \times 2.5198420997897464 \approx 0.8617738760127535 \)[/tex].
Therefore, the value of [tex]\((25)^{-\frac{1}{3}} \times \sqrt[3]{16}\)[/tex] is approximately [tex]\( 0.8617738760127535 \)[/tex].
