MCQ
Simplify $2^7\times\big(\frac{1}{8}\big)$ and write the answer in exponent form:
- A$2^{24}$
- ✓$2^4$
- C$2^3$
- D$2^5$
✓
Answer
Correct option: B.
$2^4$
B. $2^4$
Solution:
$2^7\times\big(\frac{1}{8}\big)=2^7\times\Big(\frac{1}{2\times2\times2}\Big)$
$=2^7\times\frac{1}{2^3}$
$\Rightarrow\frac{1}{2^3}=2^{-3}$
$\Rightarrow2^7\times2^{-3}$ $ (\text{a}^\text{m} × \text{a}^\text{n} = \text{a}^{m+n})$
$= 2^{7+(-3)} $
$=2^4$
Solution:
$2^7\times\big(\frac{1}{8}\big)=2^7\times\Big(\frac{1}{2\times2\times2}\Big)$
$=2^7\times\frac{1}{2^3}$
$\Rightarrow\frac{1}{2^3}=2^{-3}$
$\Rightarrow2^7\times2^{-3}$ $ (\text{a}^\text{m} × \text{a}^\text{n} = \text{a}^{m+n})$
$= 2^{7+(-3)} $
$=2^4$
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