Answer:
[tex]\frac{49}{9}[/tex]
Step-by-step explanation:
Given
[tex](\frac{-3}{7})^{2!}[/tex]
Required
Determine the reciprocal
If a number is x, the reciprocal is: 1/x
So, the reciprocal of [tex](\frac{-3}{7})^{2!}[/tex] is:
[tex]\frac{1}{(\frac{-3}{7})^{2!}}[/tex]
[tex]2! = 2*1 =2[/tex]
So, we have:
[tex]\frac{1}{(\frac{-3}{7})^{2}}[/tex]
[tex]\frac{1}{(\frac{-3^{2}}{7^{2}})}[/tex]
Evaluate all exponents
[tex]\frac{1}{(\frac{9}{49})}[/tex]
Take inverse of 9/49
[tex]\frac{49}{9}[/tex]
Hence, the reciprocal of [tex](\frac{-3}{7})^{2!}[/tex] is [tex]\frac{49}{9}[/tex]
