MCQ
Simplify $2^{-7} \times\left(2^5 \div 2^9\right)$ and write the answer in exponent form:
- A$\frac{1}{2^9}$
- B$\frac{1}{2^5}$
- ✓$\frac{1}{2^{11}}$
- D$2^{11}$
✓
Answer
Correct option: C.
$\frac{1}{2^{11}}$
C. $\frac{1}{2^{11}}$
Solution:
$2^{-7} \times\left(2^5 \div 2^9\right)=2^{-7} \times\left(2^{5 \cdot 9}\right)\left(a^m \div a^n=a^{m-n}\right) $
$=2^{-7} \times 2^{-4} $
$=2^{-7+(-4)}\left(a^m \times a^n=a^{m+n}\right) $
$=2^{-11} $
$=\frac{1}{2^{11}}$
Solution:
$2^{-7} \times\left(2^5 \div 2^9\right)=2^{-7} \times\left(2^{5 \cdot 9}\right)\left(a^m \div a^n=a^{m-n}\right) $
$=2^{-7} \times 2^{-4} $
$=2^{-7+(-4)}\left(a^m \times a^n=a^{m+n}\right) $
$=2^{-11} $
$=\frac{1}{2^{11}}$
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