Question

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
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Part 1
StartFraction x Superscript 7 divided by 9 Over x Superscript 5 divided by 9 EndFraction
equals
  
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Answer 1

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:

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