When an exponent is being raised by another exponent, we just multiply the powers and keep the base the same.

In single variable algebraic equations you want to isolate the unknown variable, which is usually a letter, and in this case , then solve for it. It is generally better to do simple operations first (e.g., addition and subtraction), so you aren't left with more complicated fractions.

1. The first step would be to move the 38 to the other side of the equation by subtracting 38 from each side (adding -38).

Giving you:

1. Now to isolate , you would divide each side of the equation by 2.

Giving you:

1. In order to verify the result you can substitute your answer in for and simplify it through operations. If you get the expression 0=0 or any other true expression it is correct:

Divide by three on both sides.

Add two on both sides.

To complete the square, we will need to divide the one-third coefficient by two, which is similar to multiplying by one half, square the quantity, and add the two values on both sides.

Simplify both sides.

Factor the left side, and combine the terms on the right.

The answer is:

Recall that when an exponent is raised to another exponent, you will need to multiply the two exponents together.

Start by simplifying the numerator:

Now, place this on top of the denominator and simplify. Recall that when you divide exponents that have the same base, you will subtract the exponent in the denominator from the exponent in the numerator.

When dealing with exponents, we convert as such: . Therefore, .

Add four on both sides.

To isolate the x-variable, we will need to multiply by two thirds on both sides.

The answer is:

When finding the equation of a quadratic from its zeros, the natural first step is to recreate the factored form of a simple quadratic with those zeros. Putting aside the coefficient, a quadratic with zeros at 3 and -6 would factor to:

So you know that a possible quadratic for these zeros would be:

Now you need to determine the coefficient of the quadratic, and that’s where the point (2, -24) comes in. That means that if you plug in x = 2, the result of the quadratic will be -24. So you can set up the equation:

, where a is the coefficient you’re solving for. And you know that this is true when x = 2, so if you plug in x = 2 you can solve for a:

So a = 3. When you then distribute that coefficient of 3 across the original simple quadratic, you have:

So your quadratic is

To complete the square, the equation must be in the form:

In order to rewrite a radical as an exponent, the number in the radical that indicates the root, gets written as a fractional exponent. Distribute the exponent to both terms by multiplying it by the exponents of each term as shown below:

From this point simplify the exponents accordingly:

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

With the same base, we can now write

Subtract on both sides.