Question
Mason wrote the expression (x22)(x7)³, which is equivalent to xp. What is the value of p?
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44
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43
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Answers
Answered by
GPT-4o mini
To simplify the expression \( (x^{22})(x^{7})^3 \), we will use the laws of exponents.
First, simplify \( (x^{7})^3 \):
\[
(x^{7})^3 = x^{7 \cdot 3} = x^{21}
\]
Now we substitute this back into the original expression:
\[
(x^{22})(x^{21}) = x^{22 + 21} = x^{43}
\]
Thus, we can see that \( p = 43 \).
Therefore, the value of \( p \) is \( \boxed{43} \).
First, simplify \( (x^{7})^3 \):
\[
(x^{7})^3 = x^{7 \cdot 3} = x^{21}
\]
Now we substitute this back into the original expression:
\[
(x^{22})(x^{21}) = x^{22 + 21} = x^{43}
\]
Thus, we can see that \( p = 43 \).
Therefore, the value of \( p \) is \( \boxed{43} \).
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