If (7^2)^p = 7^6, what is the value of p? (5 points)
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To find the value of p in the equation (7^2)^p = 7^6, we can use the property of exponents that states (a^b)^c = a^(b*c).
In this case, we have (7^2)^p = 7^6. By applying the exponentiation property, we can rewrite this as 7^(2*p) = 7^6.
Since the bases are the same (both 7), we can equate the exponents, resulting in 2*p = 6.
To find the value of p, we divide both sides of the equation by 2, giving us:
2*p/2 = 6/2.
This simplifies to p = 3.
Therefore, the value of p is 3.
To find the value of p in the equation (7^2)^p = 7^6, we need to use the exponential rule for raising a power to another power, which states that (a^b)^c = a^(b*c).
In our equation, we have (7^2)^p = 7^6. Applying the exponential rule, we get 7^(2*p) = 7^6.
Now, since the bases on both sides of the equation are the same (both are 7), we can equate the exponents and solve for p.
So, we have 2*p = 6.
To isolate p, we divide both sides of the equation by 2:
2*p / 2 = 6 / 2
Thus, p = 3.
Therefore, the value of p that satisfies the equation is 3.