Rules of indices
To summarise the rules, see the table below:
| Rules of indices | |
| 1 | \({a^m} \times {a^n} = {a^{m + n}}\) |
| 2 | \({a^m} \div {a^n} = {a^{m - n}}\) |
| 3 | \({a^0} = 1\) |
| 4 | \({({a^m})^n} = {a^{m \times n}}\) |
| 5 | \({a^{ - n}} = \frac{1}{{{a^n}}}\) |
| 6 | \({a^{\frac{1}{n}}} = \sqrt[n]{a}\) |
| 7 | \({a^{\frac{m}{n}} = \sqrt[n]{a}^m}\) |
| 1 | |
| Rules of indices | \({a^m} \times {a^n} = {a^{m + n}}\) |
| 2 | |
| Rules of indices | \({a^m} \div {a^n} = {a^{m - n}}\) |
| 3 | |
| Rules of indices | \({a^0} = 1\) |
| 4 | |
| Rules of indices | \({({a^m})^n} = {a^{m \times n}}\) |
| 5 | |
| Rules of indices | \({a^{ - n}} = \frac{1}{{{a^n}}}\) |
| 6 | |
| Rules of indices | \({a^{\frac{1}{n}}} = \sqrt[n]{a}\) |
| 7 | |
| Rules of indices | \({a^{\frac{m}{n}} = \sqrt[n]{a}^m}\) |
Calculations involving scientific notation
Try the example question below.
Question
There are 5 x 109 red blood cells in 1ml of blood.
Calculate in scientific notation the number of red blood cells in 3.25 litres of blood.
\(3.25\,litres = 3250ml = 3.25 \times {10^3}\)
Therefore the calculation is:
\((3.25 \times {10^3}) \times (5 \times {10^9})\)
\(= 3.25 \times 5 \times {10^3} \times {10^9}\)
\(= 16.25 \times {10^{3 + 9}}\)
\(= 16.25 \times {10^{12}}\)
This is not in the correct form of scientific notation as 16.25 does not lie between 0 and 10
\(=1.625\times 10^{1}\times 10^{12}\)
\(= 1.625 \times {10^{13}}\) blood cells