In some of the exercises you will do, there will be multiple steps to simplifying the expression, much like in the Order of Operations. Each of these rules is a tool and all the tools can be used together to simplify expressions.

Rules of Exponents - Applying them Together

Video Source (03:43 mins) | Transcript

**Review**

- Product Rule: When the bases are the same, you add the powers.
- Quotient Rule: When the bases are the same, you subtract the powers.
- Negative Exponent Rule: Move it to the other part of the fraction (numerator or denominator) and the exponent becomes positive.
- Power Rule: Multiply the powers.
- Exponents of 0 and 1: Anything raised to the 1 is itself, anything raised to the 0 is 1.
- (−1) Raised to an Exponent: If the exponent is even, the answer is positive, if the exponent is odd, the answer is negative.
- Follow the Order of Operations (PEDMAS).

## Additional Resources

- Khan Academy: Exponent Properties 4 (03:06 mins, Transcript)
- Khan Academy: Composite Problems (07:43 mins, Transcript)

### Practice Problems

**Simplify and Evaluate the following expressions:**

- \({\text{a}}^{5}\,{\text{b}}^{3}\left ( {\text{a}}\,{\text{b}} \right )^{4}\,{\text{b}} =\) (Solution
- \(\left ({\text{x}}\,{\text{y}} \right )^{3}{\text{x}}\,{\text{y}} =\) (Solution
- \(\dfrac{{\text{x}}^{5}\,{\text{y}}^{3}\,{\text{x}}^{2}}{{\text{x}}^{6}{\text{y}}^{2}}=\) (Video Solution
- \(\dfrac{{\text{m}}^{3}\,{\text{x}}^{7}}{{\text{m}}^{3}{\text{x}}^{2}}=\) (Solution
- \(\left ( {\text{b}}^{4}\,{\text{x}}^{3}\,{\text{y}}\,{\text{b}} \right )^{2}\,{\text{x}} =\) (Video Solution
- \(\left ( {-}{\text{m}} \right )^{3}\,{\text{b}}^{2}\,{\text{mx}}^{3} =\) (Solution
- \(\left ( -3 \right )^{3}\,{\text{a}}^{2}\,{\text{b}}^{4}\left ( -2 \right )^{2} =\) (Solution

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