Question

Power and quotlent rules Simplifx. ((4b^(2))/(3a^(3)b^(5)))^(2) Write your answer using only pos

Answer 1

To simplify the given expression ((4b^(2))/(3a^(3)b^(5)))^(2), we use the power and quotient rules of exponents. First, we can simplify the expression inside the parentheses. Then, raise the simplified expression to the power of 2.

Step-by-step explanation:

To simplify the given expression ((4b^(2))/(3a^(3)b^(5)))^(2), we use the power and quotient rules of exponents. First, we can simplify the expression inside the parentheses.

1. The numerator: 4b^(2) can be written as 4b^(2) * 1.
2. The denominator: 3a^(3)b^(5) can be written as 3a^(3)b^(5).

Next, we apply the power rule of exponents to raise the entire expression to the power of 2:

1. For the numerator, we have (4b^(2))^2 = (4^2)(b^(2*2)) = 16b^(4).
2. For the denominator, we have (3a^(3)b^(5))^2 = (3^2)(a^(3*2))(b^(5*2)) = 9a^(6)b^(10).

Therefore, the simplified expression is (16b^(4))/(9a^(6)b^(10)).