Potencias (Powers)

=3.3.3.3=81

You read  as:

three to the fourth power

three to the power of 4

In this case 3 is the base and 4 is the exponent.

Especial cases

 is read as:

four to the second power

four squared (the most common)

four to the power of two

four to the square power

 is read as

five cubed (the most common)

five to the third power

five to the power of three

Laws of powers

Ejercicios de potencias en inglés

1. Calculate:

2. Reduce the powers

a)

b)

c)

3. Express the  following numbers as a power of base ten:

a) 0.1=

b) 0.001=

c) One hundredth=

d) One millionth=

Radicales (Radicals)

 is called radical, n index of the root, a radicand.

Raíz cuadrada (square root)

The opposite of squaring a number is finding its square root.

  because  

Raíz cúbica (cube root)

The opposite of cubing a number is findingits cube root.

  because 

Otras raíces (other roots)

We can also use this same pattern to calculate roots with an index number greater than 3

  because 

Ejercicios de radicales en inglés

1. Calculate:

a)

b)

c)

d)

e) =

Extraer factores del radical (moving factors outside the radical).

If an exponent is equal to the index, the factor goes outside the radical.

Examples:

Simplificar radicales (simplifying radicals).

Examples:

Potencias de radicales (Powers of radicals).

Example:

Sumar radicales (Add radicals).

Radicals can be added when they have the same index and the same radicand.

Multiplicar radicales (Multiply radicals).

To multipy radicals with the same index, you multiply the radicands.

Exercises

1. Calculate and reduce:

a)

b)

c)

d)

2. Simplify:

a) =

b)