The rule for dividing exponents is:
For exponents with the same base, you can subtract the exponents and put the difference as exponent over the base. Remember that the fraction bar acts as a division sign! Or: [tex] \frac{ a^{m} }{a^{n} } = a^{m} \div a^{n} = a^{m-n} [/tex]
For example: [tex]\frac{ a^{5} }{a^{2} } = a^{5} \div a^{2} = a^{5-2} = a^{3} [/tex]
Back to your problem:
You're asked to simplify [tex] \frac{a^{12} b^{8} }{a^{2} b^{4}} [/tex].
Use your exponent rule for dividing exponents.
[tex]\frac{a^{12} b^{8} }{a^{2} b^{4}}\\
= a^{(12-2)} b^{(8-4)}\\
= a^{10} b^{4} [/tex]
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Answer: [tex]a^{10} b^{4}[/tex]
