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