Chapter 11.5, Problem 33WE

a.

To determine

To calculate:

Value of the given expressions.

  ${\left(\frac{1}{2}\right)}^{20}$

Answer to Problem 33WE

Value of the ${\left(\frac{1}{2}\right)}^{20}$ expressions is $0.0000009537$ .

Explanation of Solution

Give information:

Expression:

  ${\left(\frac{1}{2}\right)}^{20}$

Calculation:

It is given that,

  ${\left(\frac{1}{2}\right)}^{20}$

Fact that $2$ raised to the ${10}^{th}$ power is $1024$ or approximately $1000$ .

  ${\left({\left(\frac{1}{2}\right)}^{20}\right)}^2$ which is approximately ${\left(\frac{1}{1000}\right)}^2=\frac{1}{1000000}$ on a calculator the answer is $0.0000009537$ .

Therefore, Value of the ${\left(\frac{1}{2}\right)}^{20}$ expressions is $0.0000009537$ .

b.

To determine

To calculate:

Value of the given expressions.

  ${\left(0.9\right)}^{100}$

Answer to Problem 33WE

Value of the ${\left(0.9\right)}^{100}$ expressions is $0.0000009537$ .

Explanation of Solution

Give information:

Expression:

  ${\left(0.9\right)}^{100}$

Calculation:

It is given that,

  ${\left(0.9\right)}^{100}$

Guessing the one is accurately is not easy.

So,

  $\begin{array}{l}\left(0.9\right)\left(0.9\right)=0.81\\ \left(0.8\right)\left(0.8\right)=0.64\\ \left(0.64\right)\left(0.64\right)=0.4\\ \left(0.4\right)\left(0.4\right)=0.16\\ \left(0.16\right)\left(0.64\right)=0.1\end{array}$

Adding the powers gives ${\left(0.9\right)}^{20}=0.1$ so ${\left(0.9\right)}^{100}={0.1}^5=0.00001$

Therefore, Value of the ${\left(0.9\right)}^{100}$ expressions is $0.000027$ .

c.

To determine

To calculate:

Value of the given expressions.

  ${\left(-0.8\right)}^{50}$

Answer to Problem 33WE

Value of the ${\left(-0.8\right)}^{50}$ expressions is $0.000014$ .

Explanation of Solution

Give information:

Expression:

  ${\left(-0.8\right)}^{50}$

Calculation:

It is given that,

  ${\left(-0.8\right)}^{50}$

Power of minus is sign is even so minus sign will be ignored.

Guessing the one is accurately is not easy.

So,

  $\begin{array}{l}\left(0.9\right)\left(0.9\right)=0.81\\ \left(0.8\right)\left(0.8\right)=0.64\\ \left(0.64\right)\left(0.64\right)=0.4\\ \left(0.4\right)\left(0.4\right)=0.16\\ \left(0.16\right)\left(0.64\right)=0.1\end{array}$

Therefore, Value of the ${\left(-0.8\right)}^{50}$ expressions is $0.000014$ .