Hey, remember exponents (or powers)? Those little numbers that float above other numbers or variables? Of course you do, so let's revise the various laws we've learnt about and practice using them!
Now let's put them to the test in the following problems! Remember to be mindful of your order of operations when doing these problems.
Express in the simplest exponential form: $\left(\frac{2^0}{4^2}\right)^2$(2042)2
Think: We have too many powers so let's first see if you can express it without the brackets. Also, exponential form means we need to leave the powers rather than evaluate them.
Do:
$\left(\frac{2^0}{4^2}\right)^2$(2042)2 | $=$= | $\frac{2^{0\times2}}{4^{2\times2}}$20×242×2 |
$=$= | $\frac{2^0}{4^4}$2044 | |
$=$= | $\frac{1}{4^4}$144 |
Simplify: $k^{\frac{1}{2}}\times\left(-2k^3\right)^2$k12×(−2k3)2
Think: When a negative number/variable is squared, it becomes positive again
Do:
$k^{\frac{1}{2}}\times\left(-2k^3\right)^2$k12×(−2k3)2 | $=$= | $k^{\frac{1}{2}}\times\left(-2\times k^3\right)^2$k12×(−2×k3)2 |
$=$= | $k^{\frac{1}{2}}\times\left(-2\right)^2\times k^{3\times2}$k12×(−2)2×k3×2 | |
$=$= | $k^{\frac{1}{2}}\times4\times k^6$k12×4×k6 | |
$=$= | $4k^{\frac{1}{2}+6}$4k12+6 | |
$=$= | $4k^{\frac{13}{2}}$4k132 |
Express in positive exponential form: $\frac{s^{-4}}{s^2\times s^{-5}}$s−4s2×s−5
Think: Simplify all powers before trying to convert negative exponents into their positive counterparts
Do:
$\frac{s^{-4}}{s^2\times s^{-5}}$s−4s2×s−5 | $=$= | $\frac{s^{-4}}{s^{2+\left(-5\right)}}$s−4s2+(−5) |
$=$= | $\frac{s^{-4}}{s^{-3}}$s−4s−3 | |
$=$= | $s^{-4-\left(-3\right)}$s−4−(−3) | |
$=$= | $s^{-1}$s−1 | |
$=$= | $\frac{1}{s}$1s |
Simplify the following, giving your answer with a positive exponent: $2^2\times2^2$22×22
Simplify $p^7\div p^3\times p^5$p7÷p3×p5.
Simplify the following, writing without negative exponents.
$7p^4q^{-8}\times4p^{-4}q^{-5}$7p4q−8×4p−4q−5