Solution 1.3:4a
From Förberedande kurs i matematik 1
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Because the base is the same in both factors, the exponents can be combined according to the power rules | Because the base is the same in both factors, the exponents can be combined according to the power rules | ||
- | + | {{Displayed math||<math>2^{9}\cdot 2^{-7} = 2^{9-7} = 2^{2} = 4\,</math>.}} | |
- | <math>2^{9}\ | + | |
- | + | ||
Alternatively, the expressions for the powers can be expanded completely and then cancelled out, | Alternatively, the expressions for the powers can be expanded completely and then cancelled out, | ||
- | + | {{Displayed math||<math>\begin{align} | |
- | <math>\begin{align} | + | 2^{9-7} &= 2\cdot 2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot \frac{1}{{}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2}\\[5pt] |
- | + | &= 2\cdot 2 = 4\,\textrm{.}\end{align}</math>}} | |
- | + | ||
- | & =2\ | + | |
- | \end{align}</math> | + |
Current revision
Because the base is the same in both factors, the exponents can be combined according to the power rules
\displaystyle 2^{9}\cdot 2^{-7} = 2^{9-7} = 2^{2} = 4\,. |
Alternatively, the expressions for the powers can be expanded completely and then cancelled out,
\displaystyle \begin{align}
2^{9-7} &= 2\cdot 2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot \frac{1}{{}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2\cdot {}\rlap{/}2}\\[5pt] &= 2\cdot 2 = 4\,\textrm{.}\end{align} |