Respuesta :
Answer:
[tex]2x^3\sqrt[3]{4}[/tex]
Step-by-step explanation:
We have been given an expression [tex]\sqrt[3]{4x^2} *\sqrt[3]{8x^7}[/tex] and we are asked to find the product of our given expression.
Using exponent rule of power to powers [tex](a^{mn}=(a^m)^n)[/tex] we can write [tex]8x^7[/tex] as [tex](2x^2)^3x[/tex] and [tex]4x^2=(2x)^2[/tex].
Upon substituting these values in our expression we will get,
[tex]\sqrt[3]{4x^2} *\sqrt[3]{(2x^2)^3x}[/tex]
Using exponent rule [tex]\sqrt[n]{x^m} =x^{\frac{m}{n}}[/tex] we will get,
[tex]\sqrt[3]{4x^2} *2x^2\sqrt[3]{x}[/tex]
Multiplying [tex]\sqrt[3]{x}[/tex] by [tex]\sqrt[3]{4x^2}[/tex] we will get,
[tex]\sqrt[3]{4x^3} *2x^2[/tex]
Using exponent rule [tex]\sqrt[n]{x^m} =x^{\frac{m}{n}}[/tex] we will get,
[tex]x\sqrt[3]{4}*2x^2[/tex]
[tex]x*2x^2\sqrt[3]{4}[/tex]
[tex]2x^3\sqrt[3]{4}[/tex]
Therefore, the simplest form of the product of our given expression will be [tex]2x^3\sqrt[3]{4}[/tex].
