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. \([(-5)^{2}]^{-3} = (-5)^{2 \times (-3)} = (-5)^{-6}\).
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