ALGEBRA_MILESTONE_1.pdf
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Start by simplifying the terms in the parentheses. Using the Quotient Property of Exponents, divide the two
terms that have the same base by subtracting the exponents, and .
When subtracting fract
...
ions with a common denominator, subtract across the numerators and leave the
denominator the same.
minus equals . Next, apply the Power of Property of Exponents to multiply the two exponents and
write as a single power.
times equals . Lastly, rewrite the fraction in its simplest form.
simplifies to , so the expression simplifies to .
CONCEPT
Properties of Fractional and Negative Exponents
3
Simplify the following radical expression.
RATIONALE
To simplify this expression, we can rewrite into products of smaller numbers. There are many ways to do
this, but it can help to use a perfect square, since they simplify to integers when we evaluate the square root.
is a perfect square and it is also a factor of . We can rewrite as times . Now we can use the
Product Property of Radicals to write the factors as separate radicals.
The Product Property allows us to write the radical as the product of two individual square roots. Finally, we can
evaluate the square roots.
The square root of is . The square root of cannot be simplified further. The fully simplified radical is
.
CONCEPT
Simplifying Radical Expressions
4
Theresa bought a new desktop computer. One side of the desktop screen is 14 inches and the other side is 18 inches.
What is the length of the diagonal of the desktop screen? Answer choices are rounded to the nearest inch.
23 inches
11 inches
20 inches
16 inches
RATIONALE
We can use the Pythagorean Theorem to calculate the length of a diagonal. The variables and
represent the sides of the computer, and represents the diagonal. First, substitute for and for
. (Note that we could also substitute for and for ).
Once we have the given values plugged into the Pythagorean Theorem, we can evaluate the exponents.
squared is , and squared is . Now we can add these values together.
plus is equal to . Finally, we can take the square root of both sides to find the value of .
5
a b
c a
b a b
c
When we have a squared term, such as , taking the square root of both sides will cancel this
operation.
The square root of is approximately . The length of the diagonal, rounded to the nearest inch, is 23
inches.
CONCEPT
Calculating Diagonals
5
Write the following
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