Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Answer 1

Answer:

$\frac{1}{a^{6} b^{4} }\\\frac{a^{6} }{b^{6} }\\ \frac{a^{6} }{b^{5} } \\\frac{b^{6} }{a^{6} }\\ a^{6} b^{3}$

Step-by-step explanation:

Basically when a variable with a negative exponent, such as $a^{-2}$, 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 $\frac{1}{a^{2} }$.

To demonstrate let’s solve the first problem:

$\frac{a^{-4}b^{-2} }{a^{2} b^{2} }$

Using what we just learned, we take the reciprocal and flip the sign of  $a^{-4}$ and $b^{-2}$, which are $\frac{1}{a^{4} }$ and $\frac{1}{b^{2} }$ respectively.

Therefore the equation is now:

$\frac{1}{a^{2}a^{4}b^{2}b^{2} }$

To simplify we add the exponents (only if they have the same base, or the same variable, in this case)

Therefore our answer is:

$\frac{1}{a^{6}b^{4} }$