 UPSKILL MATH PLUS

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When dividing degrees with the same base, the powers are subtracted, and the base remains unchanged.

${a}^{n}:{a}^{m}={a}^{n-m}$

Where $a\ne 0$, $$n$$ and $$m$$ are natural numbers such that n>m.
Important!
You cannot replace the value of the difference ${a}^{15}-{a}^{4}$ on ${a}^{11}$.
The formula is applied from left to right, and from right to left.
Example:
Calculate:
1. ${5}^{3}:5$

Answer: ${5}^{3}:5={5}^{3}:{5}^{1}={5}^{3-1}={5}^{2}=25$.

2. ${3}^{7}:{3}^{3}$.
Answer: ${3}^{7}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}:{3}^{3}\phantom{\rule{0.147em}{0ex}}={3}^{7-3}\phantom{\rule{0.147em}{0ex}}={3}^{4}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}=81$.

3. Simplify the expression. $\frac{{t}^{27}}{{t}^{14}}$.
Answer:$\frac{{t}^{27}}{{t}^{14}}\phantom{\rule{0.147em}{0ex}}={t}^{27}:{\phantom{\rule{0.147em}{0ex}}t}^{14}\phantom{\rule{0.147em}{0ex}}={t}^{27-14}={t}^{13}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}$.

4. Make ${2}^{7}$ as a ratio.
Answer: Exponent $$7$$ can be represented as a difference in several ways:
$\begin{array}{l}{2}^{7}={2}^{9-2}={2}^{9}:{2}^{2};\\ \\ {2}^{7}={2}^{8-1}={2}^{8}:{2}^{1}={2}^{8}:2.\end{array}$