Question

which expression is equivalent to \frac{\left(6x^5z\
ight)^3}{4x^4z^2} ?

\bigcirc \frac{3x^4z^2}{2}
\bigcirc 54x^{11}z
\bigcirc \frac{9x^{11}z}{2}
\bigcirc 54x^{19}z^5

Explanation:

Simplify the numerator

Using the Power of a Product Rule and Exponent Rules knowledge points

$$ (6x^5z)^3 = 6^3 \cdot (x^5)^3 \cdot z^3 = 216x^{15}z^3 $$

Divide by the denominator

Using the Exponent Rules and Algebraic Simplification knowledge points

$$ \frac{216x^{15}z^3}{4x^4z^2} = \frac{216}{4} \cdot x^{15-4} \cdot z^{3-2} = 54x^{11}z $$

Answer:

• (A) \(\frac{3x^4z^2}{2}\)
• (B) \(54x^{11}z\) (Correct answer)
• (C) \(\frac{9x^{11}z}{2}\)
• (D) \(54x^{19}z^5\)