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Showing posts with label simplify. Show all posts
Showing posts with label simplify. Show all posts

### Intermediate Algebra Exam #1

Click on the 10 question exam covering topics in chapters 1 and 2. Give yourself one hour to try all of the problems and then come back and check your answers.

Solve and graph the solution set. In addition, express the solution set using interval notation.

Sketch the graph and give the domain and range.

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### Elementary Algebra Exam #1

Click on the 10 question exam covering topics in chapters 1 and 2. Give yourself one hour to try all of the problems and then come back and check your answers.

Simplify:

Solve:

Solve and graph all solutions on a number line.

10. The perimeter of a rectangle is 54 feet.  If the length is 3 feet less than twice the width, find the dimensions of the rectangle. (Set up an algebraic equation and use it to solve this problem.)

### Negative Exponents

The quotient rule for exponents can be used to define negative exponents. It might seem strange to think of negative exponents, but we need to know where they come from and how to work with them.
Factors in the numerator with a negative exponents move to the denominator.
Simplify.
If you are given a factor with a negative exponent in the denominator simply move it to the numerator. Use the following reasoning to justify this.
Simplify.

A common mistake is to multiply the base with the exponent when it is negative. For example,
Avoid this mistake . The correct solution is
Another useful property involves a rational expression raised to a negative exponent.
Simplify.
When simplifying expressions, it usually is best to simplify within the parentheses first and then apply the product and/or the quotient rule.

Simplify.
Scientific notation is an application of negative exponents. It is used to express very large or very small numbers.
An example of a power of ten might look like,
Use this to convert number expressed in scientific notation to a decimal.
Remember that we can obtain this same result by moving the decimal over six places to the right and filling in with the digit 0.

A power of ten might be negative,
Negative exponents appear when working with very small numbers.
Obtain the same result by moving the decimal over to the left 4 places.

Express the number in scientific notation.
Choose to place the decimal so that the first digit is between 1 and 10.

Multiplication is commutative, so when multiplying numbers in scientific notation multiply the decimal parts first. Next, multiply the powers of 10 using the product rule.

Multiply.
Divide.