__Powers of Monomials__

When you have an exponent raised to another exponent **(power of a power)**, simply multiply the two exponents together.

Examples:

- (3
^{2})^{2}= 3^{(2*2)}= 3^{4}- (5
^{2})^{3}= 5^{6}, since 2*3 =6- (x
^{3})^{5}= x^{15}

When you are working with multiplying numbers/variables together and then taking that product to an exponent **(power of a product)**, take the exponent to all the terms being multiplied.

Examples:

- (3x)
^{5}= 3^{5}x^{5} - (abc)
^{-3}= a^{-3}b^{-3}c^{-3}

When you combine the two methods, power of a power and power of a product, you can find the **power of a monomial**.

Examples:

- (2x
^{3})^{4}= 2^{4}x^{3*4}= 2^{4}*x^{12}= 16x^{12} - (-1x
^{5})^{2}= (-1)^{2}x^{5*2}= 1x^{10}= x^{10} - (3ab
^{9})^{2}= 3^{2}a^{2}b^{9*2}= 9a^{2}b^{18}

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Still not sure, visit here for another resource to help explain this topic.

Jay Vance

February 2006