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?
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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