Further Exercises on Square Roots

1
Compute:
$5^{3}$

$5^{3}$
$= 5 \cdot 5 \cdot 5$
$= 125$
The solution is $125$ .

$- 5^{3}$

$(- 5)^{3}$

$5^{- 3}$

$- 5^{- 3}$

${(- 5)}^{- 3}$

${(\frac{1}{2})}^{2}$
2
Handling with powers
Click on the right solution!
${(\frac{5}{3})}^{- 1} = 0.6$
${(\frac{5}{3})}^{- 1} = - \frac{5}{3}$

What is the base of the term ${(x + 2)}^{4}$ ?

Which equation is correct?
${(\frac{1}{3})}^{- 2} = 9$
${(\frac{1}{3})}^{- 2} = \frac{1}{9}$
${(\frac{1}{3})}^{- 2} = - \frac{1}{9}$
3
Is the result positive or negative? Give a reasoning for your answer.
${(- 18)}^{37} \cdot 2^{17} \cdot {(- 100)}^{18} \cdot {(- 3)}^{5}$
4
Calculate the value of the following terms.
$2^{3}$

For this task you need the following basic knowledge: Powers
$\begin{array}{l} 2^{3} = 2 \cdot 2 \cdot 2 \\ ↓ Represent the power as a product. \\ 2 \cdot 2 \cdot 2 = 8 \end{array}$
The solution is $8$ .

$(- 2)^{4}$

${(\frac{1}{2})}^{4}$

$1^{1001}$

$(- 1)^{1001}$
5
Determine whether the term is greater than or less than 1.
${(2 - 1.5)}^{(- 2)}$
6
Rewrite the following term as a single fraction. Is the absolute value greater or less than 1?
${(\frac{3}{2})}^{- 3}$
7
Is the following statement correct?

$3^{4} = 81$
8
Decrease the exponent by 1:

$3^{5}$
Note that the exponent is in the top right index, with the value 5.