Properties of the powers. Examples solved step by step.

Now we are going to study the properties of the powers.

What are the power properties for? Because they allow us to operate with the powers and thus be able to simplify much more complex expressions.

We’re going to start by defining what a power is.

What is a power

What is a power?

A power is a product of factors that are repeated a certain number of times. The repeating factor is the base and the number of times it is repeated is the exponent.

power properties

In this example, 3 is multiplied 4 times, so it reads that 3 is raised to 4.

In general it can be represented as:

potencia de una potencia

Where a is the base and n is the exponent.

Powers with negative base

A particular case of powers is when the base is negative. In this case, the result will depend on whether the exponent is even or odd. In general:

potencias con paréntesis

potencia de potencia sin parentesis

We must be very careful if the sign – is not within the parenthesis, since in that case, it is not elevated with the power, but goes to part:

power of another power

That is, the sign – is completely independent of power. We have a minus sign followed by a two squared.

We continue with the properties of the powers.

Properties of Powers

Powers with exponent one

Any value raised to 1 results in the same value:

potencia de una suma entre parentesis

Example:potencia elevada a otra potencia

Powers with zero exponent

Any value raised to 0 results in 1power of a power without parentesisExample:negative powers without parentesis

Multiplication of powers

Multiplication of powers with the same base: The base is maintained and the exponents are added:potencies properties Example:potencias con parentesis

Division of power

Division of powers with the same base: The base is maintained and exponents are subtracted:properties powersExample:powers between parentesis

Other power

High power to another power: The base is maintained and the exponents are multiplied:

potencias con base negativa sin parentesis

You can find the power without parentheses, but that is not correct. It should be in parentheses to indicate that all power is being raised to another power.

Example:potencias en parentesis

Multiplication elevated to power

Multiplication elevated to a power: This is the same as each value elevated to the same power:

todo sobre las potencias

Example:
potencia de otra potencia ejemplos

Quotient elevated to a power

Quotient elevated to a power: Is equal to the numerator and denominator elevated to the same power:

propiedades de potencias

Example:parentesis con potencias

If we can operate within the parenthesis, we can also solve the power without applying this property, only resolving the parenthesis and then elevating it to the exponent:

resolver potencias

Powers with negative exponent

Negative exponent powers: A value elevated to a negative power is equivalent to 1 divided by the value elevated to the same positive power:

potencias parentesis

Example:como se leen las potencias

As a particular case of this property is the inverse of a number, which is any value raised to -1:

empowerment with parentesis

High fraction to negative exponent: In this case the fraction is turned over and the exponent becomes positive:

potencies step by step

Rational exponent power

properties of the powerExample:

powers and parentesis

The denominator of the exponent becomes the index of the root

Rational and negative exponent power

como se lee las potencias ejemplosExample:como se hacen las potencias con parentesis