Solve for x in $2^x = 8$. What are exponential equations?
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what are indices in maths Informational
- State the quotient rule for indices.
- Simplify $\frac{p^6}{p^{-2}}$.
- Convert $\sqrt{x^3}$ to index form. How do you evaluate a number raised to a fractional power?
- How does the power of compounding relate to exponents? How are indices used in geometry (e.g., area and volume)?
- Apply the concepts in different contexts. Teach the concepts to someone else. What are some common exam questions related to indices?
- Number lines to illustrate positive and negative exponents.
- How do you apply the exponent to both the numerator and denominator of a fraction? What is a negative index?
- If linear dimensions are scaled by a factor $k$, area scales by $k^2$ and volume by $k^3$. How can you use indices to analyze the efficiency of algorithms?
- What is the limit of $a^x$ as $x \to -\infty$ for $a > 1$? What is the limit of $a^x$ as $x \to \infty$ for $0 < a < 1$?
- Change of base formula for logarithms involves indices.
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