Mason wrote the expression (x22)(x7)³, which is equivalent to xp. What is the value of p?

Question

44
45
43
47

Answer 1

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 \( \boxed{43} \).