Answer:
[tex]\frac{1}{a^{6} b^{4} }\\\frac{a^{6} }{b^{6} }\\ \frac{a^{6} }{b^{5} } \\\frac{b^{6} }{a^{6} }\\ a^{6} b^{3}[/tex]
Step-by-step explanation:
Basically when a variable with a negative exponent, such as [tex]a^{-2}[/tex], you just take the reciprocal of it and then change the exponent sign, or in simple terms flip it. The reciprocal of a^{-2} and changing the exponent sign is is [tex]\frac{1}{a^{2} }[/tex].
To demonstrate let’s solve the first problem:
[tex]\frac{a^{-4}b^{-2} }{a^{2} b^{2} }[/tex]
Using what we just learned, we take the reciprocal and flip the sign of [tex]a^{-4}[/tex] and [tex]b^{-2}[/tex], which are [tex]\frac{1}{a^{4} }[/tex] and [tex]\frac{1}{b^{2} }[/tex] respectively.
Therefore the equation is now:
[tex]\frac{1}{a^{2}a^{4}b^{2}b^{2} }[/tex]
To simplify we add the exponents (only if they have the same base, or the same variable, in this case)
Therefore our answer is:
[tex]\frac{1}{a^{6}b^{4} }[/tex]
