Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.

match each expression to make pairs of equivalent expressions.

\\(\frac{a^{-5}b^2}{ab^{-4}}\\)
\\(\frac{a^2b^2}{a^{-3}b^{-1}}\\)
\\(\frac{a^{-4}b^{-2}}{a^2b^2}\\)
\\(\frac{a^3b^{-4}}{a^{-3}b^2}\\)
\\(\frac{a^4b^{-2}}{a^{-2}b^3}\\)

tiles:
\\(\frac{b^6}{a^5}\\), \\(\frac{b^3}{a^5}\\), \\(\frac{b^6}{a^6}\\), \\(\frac{a^6}{b^6}\\), \\(a^5b^3\\), \\(\frac{1}{a^6b^4}\\), \\(\frac{a^6}{b^4}\\), \\(\frac{a^6}{b^5}\\)

Explanation:

⚡ Using what you learned: properties of exponents

Step 1: Simplify the first expression

$$ \frac{a^{-5}b^2}{ab^{-4}} = a^{-5-1}b^{2-(-4)} = a^{-6}b^6 = \frac{b^6}{a^6} $$

Step 2: Simplify the second expression

$$ \frac{a^2b^2}{a^{-3}b^{-1}} = a^{2-(-3)}b^{2-(-1)} = a^5b^3 $$

Step 3: Simplify the third expression

$$ \frac{a^{-4}b^{-2}}{a^2b^2} = a^{-4-2}b^{-2-2} = a^{-6}b^{-4} = \frac{1}{a^6b^4} $$

Step 4: Simplify the fourth expression

$$ \frac{a^3b^{-4}}{a^{-3}b^2} = a^{3-(-3)}b^{-4-2} = a^6b^{-6} = \frac{a^6}{b^6} $$

Step 5: Simplify the fifth expression

$$ \frac{a^4b^{-2}}{a^{-2}b^3} = a^{4-(-2)}b^{-2-3} = a^6b^{-5} = \frac{a^6}{b^5} $$

Answer:

The correct matches are:

*

$$\frac{a^{-5}b^2}{ab^{-4}} \longleftrightarrow \frac{b^6}{a^6}$$

*

$$\frac{a^2b^2}{a^{-3}b^{-1}} \longleftrightarrow a^5b^3$$

*

$$\frac{a^{-4}b^{-2}}{a^2b^2} \longleftrightarrow \frac{1}{a^6b^4}$$

*

$$\frac{a^3b^{-4}}{a^{-3}b^2} \longleftrightarrow \frac{a^6}{b^6}$$

*

$$\frac{a^4b^{-2}}{a^{-2}b^3} \longleftrightarrow \frac{a^6}{b^5}$$