Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. match the correct expression to the correct solution. tiles: $a^{(m + n)}$, $a^{(m div n)}$, $-a^m$, $a^{(m^n)}$, $\frac{1}{a^m}$, $a^{(m - n)}$, $a^{(m \times n)}$; expressions to match: $(a^m)^n$, $a^m \times a^n$, $a^{-m}$, $a^m div a^n$

Explanation:

Step1: Analyze \((a^m)^n\)

Using the power - of - a - power rule, \((a^m)^n=a^{m\times n}\). So \((a^m)^n\) matches with \(a^{(m\times n)}\).

Step2: Analyze \(a^m\times a^n\)

Using the product rule of exponents, when multiplying two powers with the same base, we add the exponents. So \(a^m\times a^n = a^{m + n}\).

Step3: Analyze \(a^{-m}\)

Using the definition of negative exponents, \(a^{-m}=\frac{1}{a^m}\).

Step4: Analyze \(a^m\div a^n\)

Using the quotient rule of exponents, when dividing two powers with the same base, we subtract the exponents. So \(a^m\div a^n=a^{m - n}\).

Answer:

\((a^m)^n\) \(\longleftrightarrow\) \(a^{(m\times n)}\)
\(a^m\times a^n\) \(\longleftrightarrow\) \(a^{(m + n)}\)
\(a^{-m}\) \(\longleftrightarrow\) \(\frac{1}{a^m}\)
\(a^m\div a^n\) \(\longleftrightarrow\) \(a^{(m - n)}\)