Intermediate Algebra Problems With Answers -
Sample 12 - Simplify Algebraic Expressions with Exponents

A set of intermediate algebra problems, related to simplifying algebraic expressions using the rules and properties of exponents. The solutions to these problems are at the bottom of the page.

Note: all letters used in the expressions below represent numbers that are not equal to 0.

  1. Simplify the following expressions and write them with positive exponents.

    a) x 2 x 3

    b) a -2 a -3

    c) a 5 / a 2

    d) a -3 / a 7

    e) (x 2) 3

    f) (x -2) 5

    g) (x 2 y 3) 3

    h) (x -2 y 3) 8

  2. Simplify the following expressions and write them with positive exponents.

    a) ( y 4 / y 2 ) 3

    b) ( y 4 / y -3 ) -2

    c) ( y 4 x 12 / y 2 ) 3

    d) ( y 12 x 56 / y 3 ) 0

    e) (x 2 y 4) 2 / (x y -2 ) 3

  3. Simplify the following expressions and write them with positive exponents.

    a) ( x y 2 ) 2 ( x 2 y 2 ) 2 / ( x y ) 4

    b) ( (a b 2) 3 (a 2 b 2) 4 ) 2

    c) ( x 2 y 3 ) 0 ( x 4 y 3 ) 4 / ( x y 2 ) 3

    d) ( x 3 y -2 ) 2 ( x -2 y 3 ) 4 / ( x -2 y -2 ) 3