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Important Formulas: Exponents & Powers | Mathematics (Maths) Class 8 PDF Download
Laws of Exponents
- Here are the laws of exponents when a and b are non-zero integers and m, n are any integers.
- a-m = 1/am
- am / an = am-n
- (am )n = amn
- am x bm = (ab)m
- am / bm = (a/b)m
- a0 =1
- (a/b)-m =(b/a)m
- (1)n = 1 for infinitely many n.
- (-1)p =1 for any even integer p
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FAQs on Important Formulas: Exponents & Powers - Mathematics (Maths) Class 8
| 1. What is an exponent and how is it related to powers? |  |
Ans. An exponent is a number that represents how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number. Exponents are related to powers because they indicate how many times the base number should be multiplied by itself to get the power. For example, in the expression 2^3, the base is 2 and the exponent is 3, which means 2 is multiplied by itself three times to get the power of 8.
| 2. How do you simplify expressions with exponents and powers? | |
Ans. To simplify expressions with exponents and powers, you can use the rules of exponents. These rules include multiplying powers with the same base by adding their exponents, dividing powers with the same base by subtracting their exponents, and raising a power to a power by multiplying the exponents. For example, to simplify (2^3)^2, you multiply the exponents and get 2^6, which is equal to 64.
| 3. How can I calculate the value of a power with a negative exponent? | |
Ans. When a power has a negative exponent, you can calculate its value by taking the reciprocal of the base number and changing the sign of the exponent to positive. For example, to calculate the value of 2^-3, you take the reciprocal of 2, which is 1/2, and change the exponent to positive, resulting in 1/(2^3) or 1/8.
| 4. Can you explain the zero exponent rule? | |
Ans. The zero exponent rule states that any non-zero number raised to the power of zero is equal to 1. This means that no matter what the base number is, if the exponent is zero, the result is always 1. For example, 5^0 is equal to 1 and 10^0 is also equal to 1.
| 5. How do you solve problems involving negative exponents? | |
Ans. To solve problems involving negative exponents, you can use the rule that states that any non-zero number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent. For example, to solve 4^-2, you take the reciprocal of 4^2, which is 1/16. So, 4^-2 is equal to 1/16.
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