# Exponents: Take your knowledge to a higher power

Power in Numbers

Exponents and Powers Curriculum Guide

Susan Jones

### Introduction:

According to the GED testing service, test takers struggle with “applying rules of exponents in numerical expressions with rational exponents to write equivalent expressions with rational exponents.”   (https://www.gedtestingservice.com/uploads/files/09738c12fe4e4accd9a16bab7cb99a3c.pdf )

Students do “fairly well” with simple squares and square roots, but there is a “sharp drop-off” when things get more complicated.

These are questions included in the “no calculator” portion of the test.

These skills are Mathematics Standards Level D in the College and Career Readiness Standards for Adult Education (https://www.educateiowa.gov/sites/files/ed/documents/CCRStandardsAdultEd.pdf ) under “Expressions and Equations.”

This curriculum guide will offer opportunities to build the deeper understanding necessary to understand the rules of exponents such as         (xm)^n = x^(mn)   .

Write and evaluate numerical expressions involving whole-number exponents. (6.EE.1)

Know and apply the properties of integer exponents to generate equivalent numerical expressions.  (8.EE.1)

While it may be sorely tempted to “save time” and skip to the procedural lessons, this is what leads to “sharp drop offs.”  Students will remember the simpler patterns and impose them on the more complex ones, incorrectly.   This concept is an ideal one for learning the real, understandable connections between what makes intuitive sense and more complicated math.