What is the index form of a number?
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what are indices in maths Informational
- If $y = a^x$, then $x = \log_a y$. How can you estimate the value of numbers raised to large powers?
- Groups, rings, and fields have notions of powers of elements. How are indices related to the concept of dimension in mathematics and physics?
- Assuming $(a+b)^n = a^n + b^n$.
- What happens when the base is 0 and the exponent is zero or negative? Are there any restrictions on the exponent of an index?
- Use De Moivre's Theorem to find $(1+i)^2$. Use De Moivre's Theorem to find $(\sqrt{2}(\cos(\pi/4) + i\sin(\pi/4)))^3$.
- Simplify $(\frac{2a^{-1}b^2}{4a^3b^{-4}})^3$. What are surds?
- Give an example of a physics formula using cubes. What is index notation?
- Solve the inequality $(\frac{1}{2})^x > \frac{1}{4}$. What are the graphs of exponential functions?
- What does a fractional exponent represent?
- 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?
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