Simplifying Exponential Expressions: 2^(2/3) * 2^(1/7) / 2^(1/2)

Learn how to simplify an expression with rational exponents by applying the product and quotient rules. The solution involves adding exponents in the numerator and subtracting the exponent in the denominator to reach 2^(13/42).

Answer

To solve the expression shown in the image, we use the rules of exponents:

The given expression is:

Step 1: Simplify the numerator
Using the product rule (

To add the fractions, find a common denominator, which is

So, the numerator is

Step 2: Simplify the whole expression
Now, divide by the denominator using the quotient rule (

To subtract the fractions, find a common denominator, which is

Thus, the simplified result is:

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Simplifying Exponential Expressions: 2^(2/3) * 2^(1/7) / 2^(1/2)

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