Negative Exponents Examples with Solutions
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,
16×2x = 64
Changing 16 and 64 to the power of 2
24×2x = 26 [As, 24 = 16, and 26 = 64]
Using the exponent rule,
24+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
Negative Exponents
Negative Exponents are the exponents with negative values. In other words, negative exponents are the reciprocal of the exponent with similar positive values, i.e. a-n (a negative exponent) can be understood as the reciprocal exponent as 1/an.
We can understand the concept of negative exponents by the following example, find the value of (1/2)-2 we can write this exponent as, (2/1)2 this can be further simplified as, 4/1 or 4.
Let us learn more about what are negative exponents, their examples with solutions, practice problems, and others in detail in this article.
Table of Content
- What are Negative Exponents?
- Negative Exponents Definition
- Representation of Negative Exponents
- Negative Exponent Formula
- Expressions with Negative Exponents
- Negative Exponent Rules
- Negative Exponents are Fractions
- Negative Fraction Exponents
- Multiplying Negative Exponents
- How to Solve Negative Exponents?
- Negative Exponents Examples with Solutions
- Negative Exponents Worksheet
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