Which of the following uses the properties of exponents to correctly rewrite f(x)=2⋅(513x+4)3−7 in the form f(x)=a(b)x−h+k and to determine the value of h?(1 point) Responses h=−12 h equals negative 12 h=7 h equals 7 h=12 h equals 12 h=−4
To rewrite the given function in the form f(x) = a(b)^x-h+k, we need to use the properties of exponents to simplify the expression.
First, let's rewrite 513x+4 as (5^3x+4) to bring it in the form of a base raised to an exponent.
Now, we can rewrite the equation as:
f(x) = 2 * (5^3x+4)^3 - 7
To apply the properties of exponents, we multiply the exponents when raising a power to a power. Therefore, we have:
f(x) = 2 * 5^(3 * (x+4)) - 7
Now that we have the expression in the form f(x) = a(b)^x-h+k, we need to determine the value of h.
From the above expression, we can see that the value of h is the exponent of the x term inside the parentheses. In this case, h = -(x+4) = -x - 4.
Therefore, the value of h is -4.
So, h = -4.