Question

1. which is equivalent to the expression below?

\sqrt{16x^{7}y^{4}}
a. $4x^{\frac{2}{7}}y^{\frac{1}{2}}$
c. $8x^{\frac{2}{7}}y^{\frac{1}{2}}$
b. $4x^{\frac{7}{2}}y^{2}$
d. $8x^{\frac{7}{2}}y^{2}$

Explanation:

Step1: Rewrite root as exponent

$\sqrt{16x^7y^4}=(16x^7y^4)^{\frac{1}{2}}$

Step2: Apply exponent product rule

$=16^{\frac{1}{2}} \cdot (x^7)^{\frac{1}{2}} \cdot (y^4)^{\frac{1}{2}}$

Step3: Simplify each term

$=4 \cdot x^{\frac{7}{2}} \cdot y^{2}$

Answer:

B. $4x^{\frac{7}{2}}y^{2}$