1. What are the numbers $3$ and $4$ called in the the expression $3^4$ ?
base 3
power or exponent 4
2. What is the value of $2^4$ ?
$\displaystyle 16$
3. What is the value of $2^{-1}$ ?
$\displaystyle 0\mbox{.}5$
4. Use a calculator to calculate $3^{15}$.
$14348907$
5. Express $2^2 \ × \ 2^4$ as a power to the base $2$.
$2^6$
6. Express $2^2 \ ÷ \ 2^4$ as a power to the base $2$.
$2^{-2}$
7. Express $(2^2)^3$ as a power to the base $2$.
$2^6$
8. Calculate $3^2 + 4^2$ and $(3+4)^2$.
$25$ and $49$
9. Write one million in index form to base $10$.
$10^6$
10. Write $3 \mbox{,} \, 456$ in scientific notation.
$3 \mbox{.} 456 \, × \, 10^3$
11. Write $0\mbox{.} 0123456$ in scientific notation, giving your answer to 3 significant figures.
$1 \mbox{.} 23 \, × \, 10^{-2}$
12. Why would you expect the number $\sqrt{20}$ is between $4$ and $5$.
$4^2 \mbox{ < } 20 \mbox{ < } 5^2$
13. Write $\sqrt{3}$ as a power to base $3$.
$3^{1 \mbox{/} 2}$
14. Calculate $2^{0 \mbox{.} 1}$.
$1 \mbox{.} 072$
