52 = 25
Five to the power of two equals twenty five. When you raise five to the two power, you get twenty five.
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Mathematical Explanation
Exponentiation is a mathematical operation involving two numbers, the base (x) and the exponent (y). The notation x^y represents x multiplied by itself y times. For example, 2^3 = 2 × 2 × 2 = 8. Special cases include x^0 = 1 for any non-zero x, and x^1 = x.
Frequently Asked Questions
A power (or exponent) indicates how many times to multiply a number (the base) by itself. For example, 2^3 means 2 × 2 × 2 = 8. The small number (3) is the exponent, and the larger number (2) is the base.
Any non-zero number raised to the power of 0 equals 1. For example, 5^0 = 1, 100^0 = 1, and (-3)^0 = 1. This is a fundamental rule in mathematics.
A negative exponent means to take the reciprocal of the base and then apply the positive exponent. For example, 2^(-3) = 1/(2^3) = 1/8 = 0.125.
Yes, decimal exponents are related to roots. For example, x^0.5 is the same as the square root of x, and x^0.333 is approximately the cube root of x.
Scientific notation expresses numbers as a product of a coefficient and a power of 10. For example, 1,000,000 = 1 × 10^6. Powers of 10 are fundamental to scientific notation.
Resources & References
Encyclopedia Resources
- Exponentiation - Wikipedia - Comprehensive guide to exponentiation and powers
- Exponent - Wikipedia - Learn about exponents and their properties
Educational Resources
- Khan Academy - Exponents - Free exponent lessons and practice problems
- Math is Fun - Exponents - Interactive exponent examples and explanations