(6^n)^4 = 6^-12
What is the value of n?
To solve for the value of n, we can use the property of exponents that states (a^m)^n = a^(m*n).
Therefore, we can rewrite (6^n)^4 as 6^(4n).
Since 6^(4n) = 6^(-12), we can set up the equation as follows:
6^(4n) = 6^(-12)
Since the bases are the same, we can set the exponents equal to each other:
4n = -12
Divide both sides by 4:
n = -12 / 4
n = -3
Therefore, the value of n is -3.
(8^4)^2
To find the value of (8^4)^2, we can use the property of exponents that states (a^m)^n = a^(m*n).
Therefore, we can rewrite (8^4)^2 as 8^(4*2) = 8^8.
So, the value of (8^4)^2 is 8^8, which is equal to 16,777,216.
(5+2+4)^0
To find the value of (5 + 2 + 4)^0, we simplify the expression inside the parenthesis first:
5 + 2 + 4 = 11
Now, any number raised to the power of 0 is equal to 1 (except for 0^0 which is undefined):
Therefore, (5 + 2 + 4)^0 is equal to 1.
9^-5 x 9^-3
To find the product of 9^-5 and 9^-3, we can use the property of exponents that states when multiplying two numbers with the same base, we add the exponents.
So, we can rewrite 9^-5 x 9^-3 as 9^(-5 + (-3)) = 9^-8.
Therefore, the result of 9^-5 x 9^-3 is 1/9^8, or 1/43046721.
3^-2 ÷ 3^p = 3^4
What is the value of p?
To solve for the value of p in the equation 3^-2 ÷ 3^p = 3^4, we can use the rule of exponents that when dividing the same bases, we subtract the exponents.
So, we can rewrite the equation as follows:
3^-2 / 3^p = 3^4
Next, we simplify the left side of the equation by subtracting the exponents:
3^(-2-p) = 3^4
To solve for p, we equate the exponents:
-2 - p = 4
Now, we isolate p by moving -2 to the other side of the equation:
p = -2 - 4
p = -6
Therefore, the value of p is -6.