(z^3)^? = z^-36
?=
-12
To find the value of ?, we need to equate the exponents of z on both sides of the equation.
The exponent of z on the left side is (3 * ?) and the exponent of z on the right side is -36. Therefore, we can set up the equation:
3 * ? = -36
To solve for ?, we divide both sides of the equation by 3:
(3 * ?)/3 = -36/3
? = -12
Therefore, the value of ? is -12.
To solve the equation (z^3)^? = z^-36, we can apply the rule of exponentiation.
First, we need to simplify the left side of the equation, which has a power to a power. According to the rule of exponentiation, when we raise an exponent to another exponent, we multiply the exponents: (a^b)^c = a^(b * c).
So, we can rewrite the left side of the equation as z^(3 * ?).
Now, our equation becomes z^(3 * ?) = z^-36.
Since the bases (z) are the same on both sides of the equation, we can conclude that the exponents must be equal: 3 * ? = -36.
To solve for ?, we divide both sides of the equation by 3: (3 * ?) / 3 = -36 / 3.
This simplifies to ? = -12.
Thus, the value of ? that satisfies the equation is -12.