Recall that the absolute value sign will convert any value to a positive sign. There will be no occurrences of that will evaluate into a negative one as a final solution.

There are no solutions for this equation.

The answer is:

Below is the graph of :

The given graph is the graph of reflected in the -axis, then translated up 6 units. This graph is

, where .

The function graphed is therefore

Let

The graph of this basic absolute value function is a "V"-shaped graph with a vertex at the origin, or the point with coordinates . In terms of ,

,

or, alternatively written,

The graph of is the same as that of , after it shifts 10 units left ( ), it flips vertically (negative symbol), and it shifts up 10 units (the second ). The flip does not affect the position of the vertex, but the shifts do; the vertex of the graph of is at .

Write an expression to set up the problem.

Add the ones digits.

The carryover is tens place, which is two.

Add the tens digits.

The carryover is three.

Add the hundreds places with the carryover. The two digit numbers will have zero as the hundreds places.

Combine the ones digits from each calculation.

The answer is:

In order to subtract these two numbers, we will first need to take out a common factor of negative one.

We can then subtract the terms.

Borrow a one from the tens digit to subtract the ones digits. The tens digit of 981 becomes a 7.

Borrow a one from the hundreds place to subtract the tens digits. The hundreds place of 981 becomes an eight.

Subtract the tens digits.

Subtract the hundreds digits.

The expression becomes:

The answer is:

Remember PEMDAS, the acronym that stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This is the order of operations we need to adhere to when doing any arithmetic.

The parentheses go first so do what's inside the parentheses.

The sum of and is .

Then we multiply that with to get the final answer of

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

Subtract from both sides:

When dealing with fractional exponents, remember this form:

is the index of the radical which is also the denominator of the fraction, represents the base of the exponent, and is the power the base is raised to. That value is the numerator of the fraction.

When dealing with negative exponents, we convert to fractions as such: which is the positive exponent raising base .

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.