**Simplify expression involving rational exponents :**

Here we are going to learn how to simplify expression involving rational exponents.

Rational exponents means the power is in the form fraction, to simplify expression involving rational exponents, we have to use exponent rules.

Let us see some example problems based on the above concept.

**Example 1 :**

Simplify and write the answer in positive exponents

**Solution :**

To simplify the above expression, we have to use exponent rules.

**Step 1 :**

Since we have same bases for the above terms, we have to put only one base and add the powers.

**Step 2 :**

By considering the above fractions 2/3 and 7/3, we have same denominators for both fractions. So we dont have to take L.C.M

**Step 3 :**

Hence the simplified answer is y³

**Example 2 :**

Simplify and write the answer in positive exponents

**Solution :**

To simplify the above expression, we have to use exponent rules.

**Step 1 :**

Since we have same bases for the above terms, we have to put only one base and add the powers.

**Step 2 :**

By considering the above fractions 3/5 and 7/5, we have same denominators for both fractions. So we dont have to take L.C.M

**Step 3 :**

Hence the simplified answer is a²

**Example 3 :**

Simplify and write the answer in positive exponents

**Solution :**

To simplify the above expression, we have to use exponent rules.

**Step 1 :**

Here we have common power for both terms, so we have to distribute the power 1/2.

**Step 2 :**

Whenever we have power raised to another power, we have to multiply both powers.

**Step 3 :**

By simplifying 4 and 2, we get x²

Hence the simplified answer is x² y^(1/2)

**Example 4 :**

Simplify and write the answer in positive exponents

**Solution :**

To simplify the above expression, we have to use exponent rules.

**Step 1 :**

Here we have common power for both terms, so we have to distribute the power 2.

**Step 2 :**

Whenever we have power raised to another power, we have to multiply both powers.

**Step 3 :**

By simplifying 2 and 2, we get a

Hence the simplified answer is a b^(2/3)

**Example 5 :**

Simplify and write the answer in positive exponents

**Solution :**

To simplify the above expression, we have to use exponent rules.

**Step 1 :**

In the first step we have multiplied the numbers.

**Step 2 :**

Now we have to multiply a^1/2 and a. Since both are having same base, we have to put only one base and add the powers.

**Step 3 :**

By adding a^1/2 with a^1, we get a^3/2.

Hence the simplified answer is 6 a^(3/2)

After having gone through the stuff given above, we hope that the students would have understood "Simplify expression involving rational exponents".

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