Simplifying Expressions with Fractional and Negative Exponents

Published on March 3, 2026

Algebra

This problem involves simplifying an algebraic expression by dividing terms with fractional exponents, applying the laws of exponents, and combining results.

Question

Answer

The user has provided an image containing a step-by-step mathematical simplification problem involving exponents. I will reconstruct and solve the problem based on the visible steps.

The original expression appears to be:

We know that

.

Step 1: Separate the fraction into individual terms.

Substituting

:

Step 2: Simplify each term using the rule .

Term 1:

(This matches the line: )
Term 2:

(This matches the line: )
Term 3:

The next steps in the image calculate the exponent .

Step 3: Calculate the exponent for Term 3.
To subtract the fractions, find a common denominator, which is

.
The image shows the calculation for converting the denominators:

(These match the lines:

and

)

Now combine them:

(This matches the line:

)

So, the third term is

.

Step 4: Combine the simplified terms.
The expression simplifies to:

(This matches the boxed result:

)

Step 5: Rewrite the negative exponent term.
Using the rule

:

The final simplified expression is:

(This matches the final boxed result.)

The final answer is:

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