Answer:
C. [tex] \frac{3}{2} [/tex]
Step-by-step explanation:
To find the value f b, we need to compare the exponents.
The given exponential equation is:
[tex]( {x}^{2} {y}^{3} )^{3} = ( {x} {y}^{a} )^{b}[/tex]
Recall and apply the following rule of exponents.
[tex] ( {x}^{m} )^{n} = {x}^{mn}[/tex]
We apply this rule on both sides to get:
[tex]{x}^{2 \times 3} {y}^{3 \times 3} = {x}^{b} {y}^{ab}[/tex]
Simplify the exponents on the left.
[tex]{x}^{6} {y}^{9} = {x}^{b} {y}^{ab}[/tex]
Comparing exponents of the same variables on both sides,
[tex]b = 6 \: and \:\: ab = 9[/tex]
[tex] \implies \: 6b = 9[/tex]
Divide both sides by 6.
[tex]b = \frac{9}{6} [/tex]
[tex]b = \frac{3}{2} [/tex]
