Question

simplify using the 9 laws of exponents:
\frac{(2x^2yz^3)^2}{10}
options:
\frac{x^2y^4z^6}{5}
\frac{2x^2y^2z^6}{5}
\frac{2x^4y^2z^6}{5}
\frac{5x^2y^2z^6}{2}

Explanation:

Step1: Expand numerator via power rule

$$(2x^2yz^3)^2 = 2^2 \cdot (x^2)^2 \cdot y^2 \cdot (z^3)^2 = 4x^4y^2z^6$$

Step2: Simplify the fraction

$$\frac{4x^4y^2z^6}{10} = \frac{2x^4y^2z^6}{5}$$

Answer:

$\frac{2x^4y^2z^6}{5}$ (matches the orange card option)