EmSAT Achieve Exam > EmSAT Achieve Notes > Mathematics for EmSAT Achieve > PPT: Exponents & Powers
Exponents & Powers Class 8 PPT
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Page 2 Exponents ? 3 5 base exponent 33 means that is the exponential form of t Example: he number 125 5 5 . 125 ? 5 3 means 3 factors of 5 or 5 x 5 x 5 Power Page 3 Exponents ? 3 5 base exponent 33 means that is the exponential form of t Example: he number 125 5 5 . 125 ? 5 3 means 3 factors of 5 or 5 x 5 x 5 Power The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many times the base multiplies itself. 3 Example: 5 5 5 5 ? ? ? n factors of x Page 4 Exponents ? 3 5 base exponent 33 means that is the exponential form of t Example: he number 125 5 5 . 125 ? 5 3 means 3 factors of 5 or 5 x 5 x 5 Power The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many times the base multiplies itself. 3 Example: 5 5 5 5 ? ? ? n factors of x #2: Multiplying Powers: If you are multiplying Powers with the same base, KEEP the BASE & ADD the EXPONENTS! m n m n x x x ? ?? So, I get it! When you multiply Powers, you add the exponents! 512 2 2 2 2 9 3 6 3 6 ? ? ? ? ? Page 5 Exponents ? 3 5 base exponent 33 means that is the exponential form of t Example: he number 125 5 5 . 125 ? 5 3 means 3 factors of 5 or 5 x 5 x 5 Power The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many times the base multiplies itself. 3 Example: 5 5 5 5 ? ? ? n factors of x #2: Multiplying Powers: If you are multiplying Powers with the same base, KEEP the BASE & ADD the EXPONENTS! m n m n x x x ? ?? So, I get it! When you multiply Powers, you add the exponents! 512 2 2 2 2 9 3 6 3 6 ? ? ? ? ? #3: Dividing Powers: When dividing Powers with the same base, KEEP the BASE & SUBTRACT the EXPONENTS! m m n m n n x x x x x ? ? ? ? So, I get it! When you divide Powers, you subtract the exponents! 16 2 2 2 2 4 2 6 2 6 ? ? ? ?Read More
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FAQs on Exponents & Powers Class 8 PPT
| 1. What is an exponent in mathematics? |  |
An exponent in mathematics is a number that indicates how many times a base number should be multiplied by itself. It is usually written as a superscript to the right of the base number. For example, in the expression 2^3, the base number is 2 and the exponent is 3. It means that 2 should be multiplied by itself 3 times, resulting in 2 x 2 x 2 = 8.
| 2. How do exponents simplify calculations? | |
Exponents simplify calculations by representing repeated multiplication in a concise way. Instead of writing out the product of the base number multiple times, we can use exponents to signify the repetition. For example, 2^4 is a shorthand notation for 2 x 2 x 2 x 2. This simplifies calculations and makes them easier to work with, especially when dealing with large numbers.
| 3. What are the rules for multiplying and dividing numbers with exponents? | |
When multiplying numbers with exponents, we can add the exponents if the base numbers are the same. For example, (2^3) x (2^2) = 2^(3+2) = 2^5.
When dividing numbers with exponents, we can subtract the exponent of the denominator from the exponent of the numerator if the base numbers are the same. For example, (2^5) / (2^2) = 2^(5-2) = 2^3.
| 4. How do exponents relate to powers? | |
Exponents and powers are closely related. An exponent is the superscript number that indicates how many times a base number should be multiplied by itself. A power, on the other hand, is the result of raising a base number to an exponent. For example, in the expression 2^3, the base number is 2 and the exponent is 3. The power is the value obtained by multiplying 2 by itself 3 times, which is 8.
| 5. Can exponents be negative or fractional? | |
Yes, exponents can be negative or fractional. A negative exponent indicates the reciprocal of the base number raised to the positive exponent. For example, 2^-3 is equal to 1 / (2^3) = 1 / (2 x 2 x 2) = 1/8.
A fractional exponent represents the root of the base number raised to the numerator and the denominator of the fractional exponent. For example, 4^(1/2) is equal to the square root of 4, which is 2.
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