95(12) + 24x = 5340
solve for x
Simplify the following using properties of exponents. Leave answers as powers.
6^2.2^2.3^2 =
To solve the equation 95(12) + 24x = 5340 for x, we need to isolate x on one side of the equation.
Step 1: Simplify the equation
Multiply 95 and 12: 1140 + 24x = 5340
Step 2: Move the constant term to the other side
Subtract 1140 from both sides of the equation: 24x = 4200
Step 3: Solve for x
Divide both sides of the equation by 24: x = 175
Therefore, the solution to the equation is x = 175.
Now let's simplify the expression 6^2.2^2.3^2 using properties of exponents.
First, let's break down the expression using the power of a product property:
6^2.2^2.3^2 can be written as (6^2)(2^2)(3^2)
Next, let's calculate the values:
6^2 = 6 * 6 = 36
2^2 = 2 * 2 = 4
3^2 = 3 * 3 = 9
Now, substitute these values back into the expression:
(6^2)(2^2)(3^2) = (36)(4)(9)
Finally, multiply the numbers together:
(36)(4)(9) = 1296
Therefore, the simplified expression is 1296.