Mastering the Basics: Understanding Exponents and Applying Fundamental Rules in Math

exponent

An exponent in math is a small number written to the right and above another number or expression called the base

An exponent in math is a small number written to the right and above another number or expression called the base. It indicates the number of times the base should be multiplied by itself.

For example, in the expression 2^3, the base is 2 and the exponent is 3. This means that we need to multiply 2 by itself 3 times. So, 2^3 = 2 x 2 x 2 = 8.

Exponents can also be negative or fractional. A negative exponent indicates that the base should be divided by itself multiple times. For example, in the expression 5^-2, the base is 5 and the exponent is -2. This means we need to divide 1 by 5 twice: 5^-2 = 1/(5 x 5) = 1/25.

A fractional exponent indicates that the base should be raised to a power and then take the root of that result. For example, in the expression 4^(1/2), the base is 4 and the exponent is 1/2. This means we need to take the square root of 4: 4^(1/2) = √4 = 2.

Exponents follow certain rules. Here are a few important ones:

1. Product rule: When multiplying two numbers with the same base but different exponents, you can add the exponents. For example, 2^3 x 2^4 = 2^(3+4) = 2^7 = 128.

2. Quotient rule: When dividing two numbers with the same base but different exponents, you can subtract the exponents. For example, 5^6 ÷ 5^2 = 5^(6-2) = 5^4 = 625.

3. Power rule: When raising a number with an exponent to another exponent, you can multiply the exponents. For example, (3^2)^3 = 3^(2×3) = 3^6 = 729.

4. Zero exponent rule: Any number (except 0) raised to the power of 0 is equal to 1. For example, 5^0 = 1.

These are some basic concepts and rules related to exponents. Understanding and applying them can help you solve various math problems involving exponents.

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