Answer:
\(2\times 3\)
Step-by-step explanation:
We have been given an expression and we are asked to find the cube root of our given expression.
\(\sqrt[3]{8\times 27}\)
Using the property for radicals \(\sqrt[n]{a\times b}=\sqrt[n]{a}\times \sqrt[n]{b}\) we can rewrite our expression as:
\(\sqrt[3]{8}\times \sqrt[3]{27}\)
We can rewrite terms of our given expression as:
\(8=2^3\)
\(27=3^3\)
Now, we will substitute back these terms back in our given expression.
\(\sqrt[3]{2^3}\times \sqrt[3]{3^3}\)
Using exponent property \(\sqrt[n]{x^m}=x^{\frac{m}{n}}\), we can rewrite our expression as:
\(2^{\frac{3}{3}}\times 3{\frac{3}{3}}\)
\(2^{1}\times 3^{1}\)
\(2\times 3\)
Therefore, the cube root of our given expression is \(2\times 3\).
