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The expression (x22)(x7)3(𝑥22)⁢(𝑥7)3 is equivalent to xp𝑥𝑝. What is the value of p?

Question

The expression (x22)(x7)3(𝑥22)⁢(𝑥7)3 is equivalent to xp𝑥𝑝. What is the value of p?

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Solution

The expression given is (x^22)(x^7)^3.

First, simplify the expression using the rule of exponents that states (a^m)^n = a^(m*n).

So, (x^7)^3 becomes x^(7*3) = x^21.

Now the expression is (x^22)(x^21).

Then, use the rule of exponents that states a^m * a^n = a^(m+n).

So, (x^22)(x^21) becomes x^(22+21) = x^43.

Therefore, the expression is equivalent to x^p where p = 43.

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