
PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoProduct law
The product law states that the exponents can be added when multiplying two powers with the same base.
a^{m} \times a^{n} = a^{m + n}, where a \ne 0 and a, m, n are integers.
Example:
1. 3^4 \times 3^2
Here, the base 3 is the same for both the numbers. So, we can add the powers.
a^{m} \times a^{n} = a^{m + n}
3^4 \times 3^2 = 3^{4 + 2} = 3^{6}
2. 5^{-4} \times 5^{-2}
Method I:
5^{-4} \times 5^{-2} =
=
= = = 5^{-6}
Thus, 5^{-4} \times 5^{-2} = 5^{-6}.
Method II:
5^{-4} \times 5^{-2} = 5^{(-4)+(-2)} = 5^{-6}
Quotient law
The quotient law states that we can divide two powers with the same base by subtracting the exponents.
, where a \ne 0 and a, m, n are integers.
Example:
1.
2.
= (-4)^{6+2} = (-4)^{8}
Therefore, .
Power law
The power law states that when a number is raised to a power of another power, we need to multiply the powers or exponents.
(a^m)^n = a^{mn}, where a \ne 0 and a, m, n are integers.
Example:
1. (5^2)^3 = (5)^{2 \times 3} = 5^{6}.
2. [5^{(-2)}]^3 = 5^{(-2) \times 3} = (5)^{-6}.
3. [(-5)^{2}]^{3} = (-5)^{2 \times 3} = (-5)^{6}.
4. [(-5)^{2}]^{-3} = (-5)^{2 \times (-3)} = (-5)^{-6}.