Exponents are a basic yet vital mathematical concept, representing the repeated multiplication of the same number. In an expression like “a to the power of n”, “a” is the base and “n” is the exponent. The exponent tells us how many times we multiply the base by itself. For example, “3 to the power of 4” means multiplying 3 by itself four times (3 multiplied by 3, then again by 3, and once more by 3).
Basic Concept:
- Exponent: The number that tells us how many times the base is multiplied by itself.
- Base: The number being multiplied.
Simple Examples:
- 2 to the power of 3: This means multiplying 2 by itself three times, which equals 8 (2 multiplied by 2, and then by 2 again).
- 5 to the power of 2: Known as “5 squared”, this is 5 multiplied by 5, which equals 25.
Special Cases:
- Any number to the power of 1 remains the same. For example, 7 to the power of 1 is 7.
- Any number to the power of 0 equals 1. For example, 4 to the power of 0 is 1.
Negative Exponents:
A negative exponent, like “2 to the power of -3”, means dividing 1 by the base raised to the corresponding positive exponent. So, “2 to the power of -3” equals 1 divided by 2, then divided by 2 again, and once more by 2, which is 1/8.
Fractional Exponents:
These indicate roots. For example, “9 to the power of 1/2” is the square root of 9, which equals 3.
Practice Problems:
- Calculate “4 to the power of 3”.
- What is the value of “10 to the power of -2”?
- How would you represent the cube root of 8 in exponent form?
Further Learning and Tools:
- For a deeper understanding of exponents, visit an authoritative resource like Khan Academy’s Exponent Guide.
- To quickly solve exponent problems, especially complex ones, use an online tool like the Exponent Calculator at Insight From Data.