Question

Practice Question 1 of 5 Select the correct answer. Which expression is equivalent to the (4xy³)/(x²)²

Answer 1

To simplify the expression (4xy³)/(x²)², we apply the rule of powers to simplify the denominator to x^4, then divide the coefficients and subtract the exponents of corresponding variables. The simplified expression is 4y³/x³.

Step-by-step explanation:

To find the equivalent expression for (4xy³)/(x²)², we must first recognize that the expression involves an exponent of an exponent. When simplifying expressions with exponents, we apply the rule of powers, namely, (a^(m))^(n) = a^(m*n). Thus, in this case, (x²)² can be simplified to x^(2*2) = x^4.

Now apply this rule to the original expression:

• First simplify the denominator: (x²)² = x^4.
• Then divide the coefficients: 4 by 1 is simply 4.
• Now divide the variables with exponents by subtracting the exponents in the denominator from the exponents in the numerator: x^1 - x^4 and y³ by y^0 since there are no y terms in the denominator.

After simplifying, we get the expression: 4y³/x³.