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Fractional Exponents Video Lecture | Quantitative Aptitude (Quant) - CAT
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FAQs on Fractional Exponents Video Lecture - Quantitative Aptitude (Quant) - CAT
| 1. What are fractional exponents and how do they work? |  |
Ans.Fractional exponents are a way to express roots using exponents. An exponent expressed as a fraction, such as \( \frac{m}{n} \), indicates both a power and a root. For example, \( x^{\frac{1}{2}} \) represents the square root of \( x \), and \( x^{\frac{3}{2}} \) means \( \sqrt{x^3} \) or \( (\sqrt{x})^3 \).
| 2. How do you convert a fractional exponent to a radical form? | |
Ans.To convert a fractional exponent to radical form, you can use the formula \( x^{\frac{m}{n}} = \sqrt[n]{x^m} \). For instance, \( x^{\frac{3}{4}} \) can be written as \( \sqrt[4]{x^3} \), where 4 is the root and 3 is the power.
| 3. What are some examples of problems that can be solved using fractional exponents? | |
Ans.Examples of problems that can be solved using fractional exponents include simplifying expressions like \( 16^{\frac{1}{4}} \), which equals 2, or solving equations such as \( x^{\frac{2}{3}} = 8 \) by rewriting it as \( x^2 = 8^3 \) and solving for \( x \).
| 4. How do you simplify expressions with fractional exponents? | |
Ans.To simplify expressions with fractional exponents, you can apply the laws of exponents. For example, to simplify \( x^{\frac{2}{3}} \cdot x^{\frac{1}{3}} \), you add the exponents: \( x^{\frac{2}{3} + \frac{1}{3}} = x^{1} = x \).
| 5. Can fractional exponents be negative, and what do they represent? | |
Ans.Yes, fractional exponents can be negative. A negative fractional exponent, such as \( x^{-\frac{m}{n}} \), indicates the reciprocal of the base raised to the corresponding positive fractional exponent. For example, \( x^{-\frac{1}{2}} = \frac{1}{x^{\frac{1}{2}}} = \frac{1}{\sqrt{x}} \).
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