Question

(x^2y^3) = (xy^a)^b

Answer 1

Answer:

C. $\frac{3}{2}$

Step-by-step explanation:

To find the value f b, we need to compare the exponents.

The given exponential equation is:

$( {x}^{2} {y}^{3} )^{3} = ( {x} {y}^{a} )^{b}$

Recall and apply the following rule of exponents.

$( {x}^{m} )^{n} = {x}^{mn}$

We apply this rule on both sides to get:

${x}^{2 \times 3} {y}^{3 \times 3} = {x}^{b} {y}^{ab}$

Simplify the exponents on the left.

${x}^{6} {y}^{9} = {x}^{b} {y}^{ab}$

Comparing exponents of the same variables on both sides,

$b = 6 \: and \:\: ab = 9$

$\implies \: 6b = 9$

Divide both sides by 6.

$b = \frac{9}{6}$

$b = \frac{3}{2}$