Rational Exponents (Practice Questions)

Rational exponents are exponents written as fractions, where the numerator represents the power and the denominator represents the root.

Solved Examples

Example 1: Simplify 8^{2/3}

To simplify 8^{2/3}

We rewrite 8 as 2³

so we have (2³)^{2/3}

Applying the power of a power rule,

we get 2^{{3 × (2/3)}}

= 2² = 4

Example 2: Evaluate 27^{-2/3}

To evaluate 27^{-2/3}

We rewrite 27 as (3³)

So, we have (3³)^{-2/3}

Using the power of a power rule,

we get 3^{{3 × (-2/3)}}

= 3^{-2} = 1/9

Example 3: Simplify 16^3/2

To evaluate 16^3/2

We rewrite 16 as {2⁴}

So, we have {2⁴}^3/2

Using the power of a power rule,

We get 2^{{4 × (3/2)}}

= 2^{{2 × 3}}

= 2^{6} = 64

Example 4: Calculate the values of 25^1/2

To evaluate 25^1/2

 We rewrite 25 as {5²}

So, we have {5²}^1/2

Using Power of a power rule,

= 5^{{2 × (1/2)}} = 5

Example 5: Simplify the expression: 81^3/4

To evaluate 81^3/4

We rewrite 81 as {3⁴}

So, we have {3⁴}^3/4

Using the power of a power rule,

we get 3^{{4 × (3/4)}}

= 3^{3} = 27

Practice Questions

Q1. Simplify the expression: 27^5/3

Q2. Calculate the value of expression: 8^1/3

Q3. Evaluate the expression: 16^3/4

Q4. Simplify the expression: 4^3/2

Q5. Find the value of the expression: 81^5/4