Solution 1.3:4c
From Förberedande kurs i matematik 1
(Difference between revisions)
m (Robot: Automated text replacement (-[[Bild: +[[Image:)) |
m |
||
(2 intermediate revisions not shown.) | |||
Line 1: | Line 1: | ||
- | {{ | + | The whole expression consists of factors having a base of 5 so the power rules can be used to simplify the expression first |
- | + | ||
- | {{ | + | {{Displayed math||<math>\begin{align} |
+ | \frac{5^{12}}{5^{-4}}\cdot \bigl( 5^{2} \bigr)^{-6} | ||
+ | &= \frac{5^{12}}{5^{-4}}\cdot 5^{2\cdot (-6)}\\[3pt] | ||
+ | &= \frac{5^{12}}{5^{-4}}\cdot 5^{-12}\\[3pt] | ||
+ | &= \frac{5^{12}\cdot 5^{-12}}{5^{-4}}\\[3pt] | ||
+ | &= \frac{5^{12-12}}{5^{-4}}\\[3pt] | ||
+ | &= \frac{5^{0}}{5^{-4}}\\[3pt] | ||
+ | &= 5^{0-(-4)}\\[3pt] | ||
+ | &= 5^{4}\\[3pt] | ||
+ | &= 5\cdot 5\cdot 5\cdot 5\\[3pt] | ||
+ | &= 625\,\textrm{.} | ||
+ | \end{align}</math>}} |
Current revision
The whole expression consists of factors having a base of 5 so the power rules can be used to simplify the expression first
\displaystyle \begin{align}
\frac{5^{12}}{5^{-4}}\cdot \bigl( 5^{2} \bigr)^{-6} &= \frac{5^{12}}{5^{-4}}\cdot 5^{2\cdot (-6)}\\[3pt] &= \frac{5^{12}}{5^{-4}}\cdot 5^{-12}\\[3pt] &= \frac{5^{12}\cdot 5^{-12}}{5^{-4}}\\[3pt] &= \frac{5^{12-12}}{5^{-4}}\\[3pt] &= \frac{5^{0}}{5^{-4}}\\[3pt] &= 5^{0-(-4)}\\[3pt] &= 5^{4}\\[3pt] &= 5\cdot 5\cdot 5\cdot 5\\[3pt] &= 625\,\textrm{.} \end{align} |