Hello!
The answers are:
The possible values for x in the equation, are:
First option, [tex]5\sqrt[3]{3}[/tex]
Second option, [tex]\sqrt[3]{375}[/tex]
Why?
To solve the problem, we need to remember the following properties of the exponents and roots:
[tex]a\sqrt[n]{b}=\sqrt[n]{a^{n}*b} \\\\\sqrt[n]{a^{m} }=a^{\frac{m}{n}}\\\\(a^{b})^{c}=a^{b*c}[/tex]
Then, we are given the expression:
[tex]x^{3}=375[/tex]
So, finding "x", we have:
[tex]x^{3}=375\\\\(x^{3})^{\frac{1}{3} } =(375)^{\frac{1}{3}}\\\\x=\sqrt[3]{375}=\sqrt[3]{125*3}=\sqrt[3]{125}*\sqrt[3]{3}=5\sqrt[3]{3}[/tex]
Hence, the possible values for x in the equation, are:
First option, [tex]5\sqrt[3]{3}[/tex]
Second option, [tex]\sqrt[3]{375}[/tex]
Have a nice day!
