Question

match each expression with its simplified version using exponent properties.
expressions:
$(3)^4 \cdot (3)^3$
$(3)^4 \cdot (3)^{-3}$
$\frac{(3)^3}{(3)^4}$
$((3)^4)^3$
answers to drag and drop:
$(3)^7$
$3$
$(3)^{-1}$
$(3)^{12}$

Explanation:

Step1: Simplify \((3)^4 \cdot (3)^3\)

Using the exponent rule \(a^m \cdot a^n = a^{m + n}\), here \(a = 3\), \(m = 4\), \(n = 3\). So \((3)^4 \cdot (3)^3=3^{4 + 3}=3^7\).

Step2: Simplify \((3)^4 \cdot (3)^{-3}\)

Using the exponent rule \(a^m \cdot a^n = a^{m + n}\), here \(a = 3\), \(m = 4\), \(n=- 3\). So \((3)^4 \cdot (3)^{-3}=3^{4+( - 3)}=3^{1}=3\).

Step3: Simplify \(\frac{(3)^3}{(3)^4}\)

Using the exponent rule \(\frac{a^m}{a^n}=a^{m - n}\), here \(a = 3\), \(m = 3\), \(n = 4\). So \(\frac{(3)^3}{(3)^4}=3^{3 - 4}=3^{-1}\).

Step4: Simplify \(((3)^4)^3\)

Using the exponent rule \((a^m)^n=a^{m\times n}\), here \(a = 3\), \(m = 4\), \(n = 3\). So \(((3)^4)^3=3^{4\times3}=3^{12}\).

Answer:

• \((3)^4 \cdot (3)^3\) matches with \((3)^7\)
• \((3)^4 \cdot (3)^{-3}\) matches with \(3\)
• \(\frac{(3)^3}{(3)^4}\) matches with \((3)^{-1}\)
• \(((3)^4)^3\) matches with \((3)^{12}\)