Laws of Exponents (Practice Problems)

Laws of exponents are mathematical rules used to simplify expressions involving powers and exponents.

Solved Examples

Example 1: What is the simplification of 7³ × 7¹?

Solution:

7³ × 7¹ = 7³⁺¹ = 7⁴

Example 2: Simplify and find the value of 10²/5².

Solution:

We can write the given expression as;

10²/5²= (10/5)² = 2² = 4

Example 3: Find the value of (256)^3/4

Solution:

(256)^3/4 = (4⁴)^3/4 = 4^4×(3/4) = 4³ = 64

Example 4: Find the value of 7^-3

Solution:

7^-3 = (1/7)³ = 1³/7³ = 1/343

Example 5: Find the value of x if 125 = 25/5^x

Solution:

We have 125 = 25/5^x

 ⇒ 5³ = 5²/5^x

 ⇒ 5³ = 5^2-x

Now the quantity is the same on both sides and bases are also the same, hence, exponents will also be the same. 

⇒ 3 = 2-x

⇒ x = 2-3 = -1

Practice Problems

1. (2³)⁴

2. (5³*5²)/5⁴

3. Solve for x in the equation 3^2x = 81

4. If 2^a = 8 and 2^b = 32, find the value of a + b.

5. Solve 2^-3 × 4^-1

6. Solve for x in the equation: 5^{2x + 1} = 125

7. If 16^x-1 = 8, find the value of x.

8. (27)^2/3

9. Simplify (9/4)^(3/2)

10. Solve for x in the equation: 2^2x-1 = 8x + 1 2^(3^2)