Simplify completely.
(c6c2)5
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To simplify the expression (c6c2)5, we can multiply the exponents and combine like terms.
The expression can be written as c^6 * c^2, since the exponent outside the brackets applies to each term inside the brackets.
When we multiply two terms with the same base, we add their exponents. So, c^6 * c^2 can be simplified to c^(6+2), which is equal to c^8.
Therefore, (c6c2)5 simplifies to c^8.
To simplify the expression (c^6c^2)^5, we need to apply the rules of exponents.
First, we use the product rule of exponents, which states that (ab)^n = a^n * b^n.
In this case, c^6c^2 can be rewritten as (c^6)*(c^2).
Applying the product rule, we can simplify (c^6c^2)^5 as (c^6)^5 * (c^2)^5.
Next, we use the power rule of exponents, which states that (a^n)^m = a^(n*m).
Using the power rule, we can simplify (c^6)^5 as c^(6*5) and (c^2)^5 as c^(2*5).
Therefore, simplifying completely, (c^6c^2)^5 becomes c^30 * c^10, which can be further simplified as c^(30+10) = c^40.
So, the final answer is c^40.