Question

Simplify the expression. a)1/64 b)2^-30 c)64 d)2^30

Answer 1

$\left(\dfrac{(-1)^5}{(-2)^{-3}} \right)^2\\\\\\=\left(\dfrac{-1}{\dfrac{1}{(-2)^3}} \right)^2\\\\\\=\left(-1 \times -8\right)^2\\\\=8^2\\\\=64$

Answer 2

Answer:

$\huge\boxed{\bf\:64}$

Step-by-step explanation:

$\left(\frac{(-1)^{5}}{\left(-2\right)^{-3}}\right)^{2}$

Now, simplify $(-1)^{5} = -1$. Then,

$\left(\frac{-1}{\left(-2\right)^{-3}}\right)^{2}$

Calculate: $(-2)^{-3} = \frac{1}{(-2)^{3}} = - \frac{1}{8}$.

$\left(\frac{-1}{-\frac{1}{8}}\right)^{2}$

Divide $-1$ by $- \frac{1}{8}$. The result will be $8.$

$\left(-\left(-8\right)\right)^{2} \\= 8^{2}$

Calculate $8$ to its square which is $64.$

$8^{2}\\=\boxed{\bf\: 64} \: \:\mathrm{(3^{rd} \: option)}$

$\rule{150pt}{2pt}$