factor the algebraic expression.\nx^{5/9}-x^{1/9}\nx^{5/9}-x^{1/9}=\\square (type exponential notation with…
factor the algebraic expression.\nx^{5/9}-x^{1/9}\nx^{5/9}-x^{1/9}=\\square (type exponential notation with positive exponents.)
Answer
Explanation:
Step1: Factor out the common factor
We can factor out $x^{\frac{1}{9}}$ from both terms. So, $x^{\frac{5}{9}}-x^{\frac{1}{9}}=x^{\frac{1}{9}}(x^{\frac{5}{9}-\frac{1}{9}} - 1)$.
Step2: Simplify the exponent inside the parentheses
Calculate $\frac{5}{9}-\frac{1}{9}=\frac{5 - 1}{9}=\frac{4}{9}$. Then the expression becomes $x^{\frac{1}{9}}(x^{\frac{4}{9}}-1)$.
Answer:
$x^{\frac{1}{9}}(x^{\frac{4}{9}} - 1)$