MCQ
The value of the expression $\frac{(-1)^{101} \times(8)^5}{(4)^7}$ is equal to
- A$2$
- ✓$-2$
- C$\frac{1}{16}$
- D$-\frac{1}{16}$
✓
Answer
Correct option: B.
$-2$
$\frac{(-1)^{101} \times(8)^5}{(4)^7}$
$=\frac{(-1)^{101} \times\left(2^3\right)^5}{\left(2^2\right)^7}$
$=\frac{-1 \times 2^{3 \times 5}}{2^{2 \times 7}}$
$=\frac{-1 \times 2^{15}}{2^{14}}$
$=-1 \times 2^{15-14}$
$=-1 \times 2$
$=-2$
$=\frac{(-1)^{101} \times\left(2^3\right)^5}{\left(2^2\right)^7}$
$=\frac{-1 \times 2^{3 \times 5}}{2^{2 \times 7}}$
$=\frac{-1 \times 2^{15}}{2^{14}}$
$=-1 \times 2^{15-14}$
$=-1 \times 2$
$=-2$
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