match each expression with its simplified version using exponent properties. \nexpressions: \n$(3)^4 \\cdot…

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

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

Answer

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})