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calculista

There are a couple of operations you can do on powers

We can multiply powers with the same base

x4⋅x2=(x⋅x⋅x⋅x)⋅(x⋅x)=x6

xa⋅xb=xa+b

This is an example of the product of powers property tells us that when you multiply powers with the same base you just have to add the exponents.

Edufirst
Answer: the property that tells to multiply the powers to simplify is called power of a power.


Explanation:

This is when you have an expression of the kind: [tex]( x^{m} )^n[/tex]

It is equal to: [tex]( x^{m.n} )[/tex]

[tex]( x^{m} )^n = x^{m.n} [/tex]

Some examples will help you to understand and remember better:

[tex]( x^{2} )^5= x^{2.5} =x^{10}[/tex]

[tex] (10^{3} )^4=10^{3.4}=10^{12}=1,000,000,000,000[/tex]

[tex] (4^{3} )^2=4{3.2}=4^{6}=4,096[/tex]

Remember a power raised to the power is a property named power of a power and tells that you keep the base and multiply the powers.