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Simplify.
Rewrite the expression in the form y^n.
(y^2)^3 =

User Mducc
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3 votes

Answer:


y^6

Explanation:

So there is an exponent identity that states:
(x^b)^a = x^(a*b) which means this question becomes:
(y^2)^3 = y^(2*3) = y^6.

Just so you completely understand why this works, it might help to express y^2, as what it truly represents:
y^2=y*y. So using this definition we can substitute it into the equation so it becomes:
(y*y)^3. Now let's use the definition of exponents like we just did with the y, to redefine this in terms of multiplication:
(y*y)^3 = (y * y) * (y * y) * (y * y). We can just multiply all these out, and we get:
y * y * y * y * y * y =y^6.

To make it a bit more general when we have the exponent:
x^b it can be expressed as:
(x*x*x...\text{ b amount of times}) now when we raise it to the power of a. we get:
(x * x * x...\text{ b amount of times})^a which can further be rewritten using the definition of an exponent to become the equation:
(x*x*x\text... \text{ b amount of times}) * (x * x * x...\text{ b amount of times})...\text{ a amount of times} which just simplifies to:
x*x*x*x...\text{ a times b amount of times}. Hopefully this makes the identity a bit more understandable

User Sean Wessell
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