Raising+a+Power+to+a+Power

Raising a power to a power means that we have an exponent that is being raised to another exponent. For example:



To simplify these expressions, we start with the power furthest outside. Since the parentheses are used to group things together, we will begin with the exponent outside the parentheses. The exponent outside the parentheses tells us how many times we have to multiply the base (the quantity inside the parentheses) by itself.

Going back to our examples above that means that:



Now, using what we know about multiplying exponents, we can find the products.

**TASK: How do we raise a power to another power?**

To finish simplifying, we get:



There is a shortcut. Look at the example problems above and see if you can find it. Look specifically at the bases and the exponents and see what you have to do to get from the base and exponents in the original problem to the base and the exponents in the answer.
 * Is there a shortcut?**

**TASK: What shortcut did you find?**

**TASK: Open the document and complete the practice problems. **