order the expressions from least value to greatest value. \n$left(3^{2}\right)^{2}$ \n$2^{2} cdot 2^{3}$…

order the expressions from least value to greatest value. \n$left(3^{2}\right)^{2}$ \n$2^{2} cdot 2^{3}$ \n$left(\frac{5}{2}\right)^{3}$ \n$\frac{6^{1002}}{6^{1000}}$

order the expressions from least value to greatest value. \n$left(3^{2}\right)^{2}$ \n$2^{2} cdot 2^{3}$ \n$left(\frac{5}{2}\right)^{3}$ \n$\frac{6^{1002}}{6^{1000}}$

Answer

Answer:

$\frac{6^{1002}}{6^{1000}}$, $\left(\frac{5}{2}\right)^3$, $2^2 \cdot 2^3$, $(3^2)^2$

Explanation:

Step1: Simplify each expression

  • $(3^2)^2 = 3^{2 \times 2} = 3^4 = 81$
  • $2^2 \cdot 2^3 = 2^{2+3} = 2^5 = 32$
  • $\left(\frac{5}{2}\right)^3 = \frac{5^3}{2^3} = \frac{125}{8} = 15.625$
  • $\frac{6^{1002}}{6^{1000}} = 6^{1002-1000} = 6^2 = 36$

Step2: Order from least to greatest

Compare values: $15.625 < 36 < 32 < 81$ → $\left(\frac{5}{2}\right)^3 < \frac{6^{1002}}{6^{1000}} < 2^2 \cdot 2^3 < (3^2)^2$