General Mathematics - Index Laws Class 8

Using exponent rules: (1/2)^1 / (1/2)^0 * (1/2)^2. Since (1/2)^0 = 1, the expression becomes (1/2)^1 * (1/2)^2. Adding the exponents (1+2) gives (1/2)^3.

The expression (4^3)^2 equals 4^(3*2) = 4^6. Options A (4^6), B (4^6), and D (4^6) are equivalent. Option C is 4^5, which is not equal to 4^6.

Any non-zero number raised to the power of 0 is 1. Therefore, 5^0 = 1 and 9^0 = 1. The product 1 * 1 = 1.

By definition, any non-zero number raised to the power of 0 is 1. This is a fundamental rule of exponents.

When dividing terms with the same base, you subtract the exponents. Here, 5^3 divided by 5^1 equals 5^(3-1), which is 5^2.

Any number raised to the power of 1 remains unchanged. This is because the base is used as a factor exactly once.

Index Law 2 states that when dividing powers with the same base, you subtract the exponents. Therefore, a^m divided by a^n equals a^(m-n).

When multiplying powers with the same base, you add the exponents. Thus, 3^4 times 3^2 equals 3^(4+2), which is 3^6.

An exponent indicates how many times the base is multiplied by itself. 2^6 means 2 is multiplied by itself 6 times.

Index Law 1 states that when multiplying terms with the same base, you add the exponents. So, a^m times a^n equals a^(m+n).

The terms index, exponent, and power are often used interchangeably to describe the number that indicates how many times the base is used as a factor.

In the expression 4^7, the number 4 is the base and the number 7 is the index (or exponent).

In an exponential expression like 3^6, the base is the number being multiplied, which is 3.

Writing a number as a base raised to an exponent is known as index notation or exponential notation.

Since 2 is multiplied by itself 4 times, it is written as 2 raised to the power of 4, or 2^4.