Objective You will apply the properties of exponents to write equivalent numerical expressions.

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Properties of Exponents

Answer the following questions. Be sure to show all your work.

1. Divide . Write the quotient as one power. The variable is not equal to zero.

2. If it requires x to the power of 4 silkworms to produce enough silk to make a scarf in a given amount of time, but it requires x to the power of 19 silkworms to produce enough silk to make a sheet in the same amount of time. How many times more silkworms are needed for the sheet than the scarf? Hint: Divide number of silkworms to make a sheet by the number of silkworms to make a scarf.

3. Simplify open parentheses d to the power of negative 4 end exponent close parentheses to the power of 6.

4. Simplify m to the power of 4 times n to the power of 4.

5. When multiplying powers with the same base, keep the base and multiply the exponents. Explain, in complete sentences, whether this statement is true or false, and why.