Hello!
The answer is:
The equation has only one root (zero) and its's equal to 3.
[tex]x=3[/tex]
Why?
We are working with a cubic equation, it means that there will be three roots (zeroes) for the equation.
To solve the problem, we need to remember the following exponents and roots property:
[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]
[tex](a^{b})^{c}=a^{b*c}[/tex]
So, we are given the equation:
[tex]x^{3}-27=0[/tex]
Isolating x we have:
[tex]x^{3}=27\\\\\sqrt[3]{x^{3}}=\sqrt[3]{27}\\\\x^{\frac{3}{3} }=\sqrt[3]{(3)^{3} }\\\\x^{\frac{3}{3} }=3^{\frac{3}{3} }\\\\x=3[/tex]
Hence, we have that the equation has only one root (zero) and its's equal to 3.
Have a nice day!
