Multiplying and Dividing Powers with the Same Base Worksheet with Answer Key

What's on the worksheet

1. Simplify to a single power:
   3^{5} \cdot 3^{2}x^{11} \div x^{4}d \cdot d \cdot d^{7}\dfrac{12^{10}}{12^{9}}\dfrac{u^{9}}{u^{2}} \cdot u^{4}
2. Find the whole number exponent that makes each statement true:
   6^{n} \cdot 6^{n} \cdot 6^{3} = 6^{11}\dfrac{p^{3n}}{p^{n}} = p^{12}\dfrac{x^{20}}{x^{n} \cdot x^{4}} = x^{9}2^{n} \cdot 16 = 2^{13}
3. Write each as a single power of the named base, then find its value:
   \dfrac{2^{9} \cdot 4}{32}, base 2\dfrac{3^{8}}{27}, base 3\dfrac{49 \cdot 7^{3}}{7^{4}}, base 71000 \cdot 10^{4} \div 100, base 10
4. Simplify expressions whose exponents contain n:
   \dfrac{a^{5n}}{a^{2n}}c^{n} \cdot c^{n} \cdot c^{n+1}\dfrac{b^{2n+5}}{b^{n+1}}\dfrac{y^{4n} \cdot y^{n}}{y^{3n}}
5. Decide if each statement is true or false, and correct the false ones:
   5^{3} \cdot 5^{6} = 5^{18}\dfrac{x^{12}}{x^{3}} = x^{4}2^{4} \cdot 2^{4} = 2^{8}3^{2} + 3^{2} = 3^{4}2^{5} \cdot 3^{2} = 6^{7}
6. Word problem: how many pencils are in the warehouse?
7. Explain why adding equal powers raises the exponent by one, and use it on a sum.