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Exponents & Radicals

These problems require knowledge of the rules and properties of exponents and radicals.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Algebra: Exponents
Algebra: Radicals
The closest match in our Ask Dr. Math archives:
Middle School: Exponents
Middle School: Square Roots
NCTM Standards:
Algebra Standard for Grades 912
Access to these problems requires a Membership.

The ABC's of Exponents
 Steve Risberg

Algebra, difficulty level 3. Solve a system of equations involving exponents.
... more>>

A Coat of Golden Angels
 Terry Trotter

Algebra, difficulty level 1. Show how to do scientific notation problems on an 8digit, fourfunction calculator.
... more>>

Don't Be Square
 Ethel Breuche

Algebra, difficulty level 1. Use pattern recognition and square roots to find the sum of two numbers.
... more>>

Elbert's Equation
 Steve Risberg

Algebra, difficulty level 3. Use exponent properties, absolute value, and quadratic equations to
find the six solutions to Elbert's equation.
... more>>

It's the Law!
 Terry Trotter

Algebra, difficulty level 3. Explain the two most important laws of exponents, as a good teacher or book might do.
... more>>

Polynomial Power
 Steve Risberg

Algebra, difficulty level 3. Given the value of one variable expression, can you use it to find the value of others?
... more>>

Poolish Pride?
 Steve Risberg

Algebra, difficulty level 3. Two competitive brothers build rectangular pools of similar shape but
different size. Given some information relating the lengths and
widths, find the area of the larger pool.
... more>>

A Space Diagonal
 Terry Trotter, MATHCOUNTS

Algebra, difficulty level 2. Find the space diagonal of a certain cube in a sequence of cubes.
... more>>

Two Ladders
 Terry Trotter

Algebra, difficulty level 2. Find the lengths of two ladders, then find their "differences."
... more>>

What's the Point?
 Steve Risberg

Algebra, difficulty level 3. Find all points on a given line such that they are a specified
distance from two points in the plane.
... more>>
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