**Multiplication of powers:**

When multiplying numbers with the same base, keep the base and add the indices.

*a ^{m }x a^{n }= a^{m+n}*

**Division of powers:**

When dividing numbers with the same base, keep the base and subtract the indices.

*a ^{m ÷} a^{n }= a^{m}/ a^{n }= a*

^{m−n }

**Power of a power:**

When raising a number in index form to a power, keep the base and multiply the indices.

*(a ^{m})^{n }= a^{mn}*

**Expanding products:**

When removing brackets around a product that has been raised to a power, raise each number to that power.

**(ab) ^{m} = a^{m}b^{m}**

**Expanding quotients:**

When removing brackets around a quotient that has been raised to a power, raise each number to that power.

**(a/b) ^{m }= a^{m}/b^{m}**

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