Give an example of a polynomial with terms involving indices. How are indices used in calculus (e.g., differentiation and integration)?
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what are indices in maths Informational
- Using the same definitions, $xy = b^m \times b^n = b^{m+n}$, so $\log_b (xy) = m+n = \log_b y + \log_b x$. Can you explain the quotient rule for logarithms using the quotient rule for indices?
- Misapplying the power of a power rule. Are there any historical aspects to the development of index notation?
- Applications in calculus and beyond. What are some common misconceptions about indices that students often have?
- What happens when the base is 1? Can the base be 0?
- How do you evaluate a number raised to a negative power? What is the value of $2^{-3}$?
- Evaluate $\log_3 9$ using the definition of logarithms and indices. How are indices used in solving simultaneous equations where variables are in the exponents?
- How do you apply the exponent to each factor in a product? What is the fifth law of indices?
- Matrix transformations often involve powers and combinations. How are indices used in data compression algorithms? How are indices used in machine learning algorithms? What are some open problems or active areas of research involving exponents or related concepts? Are there different conventions for index notation in different parts of the world or in different fields? How do indices relate to the concept of order of magnitude?
- What does $a^{bi}$ represent?
- Evaluate $(5 - 2)^3 + 1$.
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