Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Simplify the expression:

[tex](25)^{-\frac{1}{3}} \times \sqrt[3]{16}[/tex]

Sagot :

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].