Class 7 Exam > Class 7 Videos > Mathematics (Maths) Class 7 (Old NCERT) > Laws of Exponents
Laws of Exponents Video Lecture | Mathematics (Maths) Class 7 (Old NCERT)
FAQs on Laws of Exponents Video Lecture - Mathematics (Maths) Class 7 (Old NCERT)
| 1. What are the basic laws of exponents that I need to know? |  |
Ans.The basic laws of exponents include the Product of Powers (when multiplying like bases, add the exponents), the Quotient of Powers (when dividing like bases, subtract the exponents), the Power of a Power (when raising an exponent to another exponent, multiply the exponents), the Power of a Product (when raising a product to an exponent, distribute the exponent to each factor), and the Power of a Quotient (when raising a quotient to an exponent, distribute the exponent to the numerator and denominator).
| 2. How do I simplify expressions using the laws of exponents? | |
Ans.To simplify expressions using the laws of exponents, identify the like bases and apply the appropriate law. For example, in the expression \( a^m \cdot a^n \), you would add the exponents to get \( a^{m+n} \). Similarly, for \( \frac{a^m}{a^n} \), subtract the exponents to get \( a^{m-n} \). Always be mindful of the base and whether exponents are positive or negative.
| 3. Can you explain the law of negative exponents? | |
Ans.The law of negative exponents states that \( a^{-n} = \frac{1}{a^n} \) for any non-zero base \( a \) and any positive exponent \( n \). This means that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent.
| 4. What is the zero exponent rule in exponents? | |
Ans.The zero exponent rule states that any non-zero base raised to the power of zero equals one, i.e., \( a^0 = 1 \) for \( a \neq 0 \). This rule holds true for all non-zero numbers, and it is important to remember that zero raised to any exponent is undefined.
| 5. How can I apply the laws of exponents in solving algebraic equations? | |
Ans.To apply the laws of exponents in algebraic equations, use them to rewrite and simplify expressions. For example, if you have an equation like \( 2^x \cdot 2^3 = 32 \), you can simplify the left side to \( 2^{x+3} = 32 \). Since \( 32 \) can be rewritten as \( 2^5 \), you can set the exponents equal to each other: \( x + 3 = 5 \), leading to \( x = 2 \).
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