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The given expression is:

\[
x^{\frac{7}{8}} \cdot x^{-\frac{2}{3}}
\]

To simplify this, we can apply the rule of exponents that states:

\[
x^a \cdot x^b = x^{a+b}
\]

In this case, the exponents are \( \frac{7}{8} \) and \( -\frac{2}{3} \). Let's add these exponents together.

\[
\frac{7}{8} + \left( -\frac{2}{3} \right) = \frac{7}{8} - \frac{2}{3}
\]

To add these fractions, we need a common denominator. The least common denominator of 8 and 3 is 24, so we rewrite both fractions:

\[
\frac{7}{8} = \frac{21}{24}, \quad \frac{2}{3} = \frac{16}{24}
\]

Now subtract the second fraction from the first:

\[
\frac{21}{24} - \frac{16}{24} = \frac{5}{24}
\]

Thus, the simplified expression is:

\[
x^{\frac{5}{24}}
\]

Would you like further details or clarification on this? Here are 5 related questions for practice:

1. What is the simplified form of \( x^{\frac{3}{4}} \cdot x^{-\frac{5}{6}} \)?
2. How do you handle the multiplication of terms with negative exponents?
3. What is the least common denominator between \( \frac{3}{5} \) and \( \frac{2}{7} \)?
4. Can you simplify \( x^a \cdot x^b \cdot x^c \)?
5. What is the general rule for multiplying two powers of the same base?

**Tip:** Always look for the least common denominator when adding or subtracting fractions with different denominators.

Learn how to simplify expressions with exponents, specifically x^(7/8) · x^(-2/3). This guide covers key exponent rules, fraction addition, and simplification techniques suitable for Grades 8-10.

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