Factor the common factor from the expression:
x^1/3; x^10/3 + x^1/3
x^(1/3)[x^(9/3)+1]
To factor out the common factor from the expression x^(1/3), we need to find the highest exponent that the variable x appears with. In this case, the highest exponent is 1/3 because x only appears with that exponent.
To factor out x^(1/3) from the expression x^(10/3) + x^(1/3), we can divide every term by x^(1/3):
x^(10/3) / x^(1/3) + x^(1/3) / x^(1/3)
When we divide x^(10/3) by x^(1/3), we subtract the exponents:
x^(10/3 - 1/3) + x^(1/3 - 1/3)
Simplifying the exponents:
x^(9/3) + x^(0/3)
Since any number raised to the power of 0 is always 1:
x^(3) + 1
Therefore, the factored form of the expression x^(10/3) + x^(1/3) is x^3 + 1.