Use properties of rational exponents to simplify the expression. Assume that all variables represent positive numbers.

StartFraction x Superscript 7 divided by 9 Over x Superscript 5 divided by 9 EndFraction
Question content area bottom
Part 1
StartFraction x Superscript 7 divided by 9 Over x Superscript 5 divided by 9 EndFraction
equals
  
enter your response here

1 answer

To simplify the expression \(\frac{x^{\frac{7}{9}}}{x^{\frac{5}{9}}}\), we can use the property of exponents that states:

\[ \frac{a^m}{a^n} = a^{m-n} \]

Applying this property to our expression:

\[ \frac{x^{\frac{7}{9}}}{x^{\frac{5}{9}}} = x^{\frac{7}{9} - \frac{5}{9}} \]

Now, we subtract the exponents:

\[ \frac{7}{9} - \frac{5}{9} = \frac{7 - 5}{9} = \frac{2}{9} \]

Therefore, we can simplify the expression to:

\[ x^{\frac{2}{9}} \]

So, the final simplified form is:

\[ \boxed{x^{\frac{2}{9}}} \]