Negative Exponents (Practice Problems)

Negative exponents are exponents with negative values. They indicate that the base is written as its reciprocal with a positive exponent.

Solved Examples

Example 1: Find the values of 7^-3 × 7³.

Solution:

7^-3 × 7³

Using the negative rule of the exponent,

1/7³ × 7³

= 7³/7³

= 1

The required solution is, 1

Example 2: Simplify for the value of x in 16/2^-x = 64.

Solution:

Given, 16/2^-x = 64

Using the negative rule of the exponent,

16×2^x = 64

Changing 16 and 64 to the power of 2

2⁴×2^x = 2⁶        [As, 2⁴ = 16, and 2⁶ = 64]

Using the exponent rule,

2^4+x = 2⁶

Now the exponents are the same as the bases are same so their power must also be the same.

4+x = 6

x = 6-4 = 2

Now the value of the x is,

x = 2

Example 3: Simplify (4/3)^-3 + (11/2)^-1.

Solution:

Using Negative Exponent Rules,

(4/3)^-3 = (3/4)³

(11/2)^-1 = (2/11)¹

= (4/3)^-3 + (2/11)¹

= (3/4)³ + (2/11)¹

= 27/64 + 2/11

= (27×11 + 2×64)/ 64×11

= (297 + 128)/704

= 425/704

The required solution is, 425/704

Practice Questions

1. Evaluate 2^-3

2. Simplify 5x^-2

3. Compute 3^-2

4. Simplify 14x−14x−11​

5. Evaluate 10^-4

6. Simplify 12y−32y−31​

7. Compute a^-4 × a²