Rationalize $\frac{2}{1+\sqrt{3}}$. Rationalize $\frac{\sqrt{5}-1}{\sqrt{5}+1}$.
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what are indices in maths Informational
- Use a calculator or software to verify results. Work backwards from the simplified form.
- Evaluate $\log_2 8$ using the definition of logarithms and indices. Evaluate $\log_{10} 1000$ using the definition of logarithms and indices.
- Simplify $(27)^{2/3}$. Can the base of an index be negative?
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- Express 72 as a product of its prime factors using indices. Express 100 as a product of its prime factors using indices.
- These units are based on powers of 2. What is the difference between exponential growth and polynomial growth?
- Evaluate $16^{3/4}$.
- If $y = b^m$ and $x = b^n$, then $\log_b y = m$ and $\log_b x = n$. $y^k = (b^m)^k = b^{mk}$, so $\log_b y^k = mk = k \log_b y$. Can you explain the product rule for logarithms using the product rule for indices?
- Working with irrational exponents. Proving identities involving indices.
- Write $a^{m/n}$ in radical form.
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