Question

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simplify $\frac{(x^{2})^{3}\cdot5x}{6x^{2}\cdot15x^{3}}$.
$\bigcirc$ $\frac{x^{2}}{18}$
$\bigcirc$ $\frac{1}{9x^{2}}$
$\bigcirc$ $18x^{2}$
$\bigcirc$ $9x^{2}$

Explanation:

Step1: Simplify numerator exponent

$(x^2)^3 = x^{2\times3} = x^6$
Numerator becomes $x^6 \cdot 5x = 5x^{6+1} = 5x^7$

Step2: Simplify denominator terms

$6x^2 \cdot 15x^3 = (6\times15)x^{2+3} = 90x^5$

Step3: Reduce the fraction

$\frac{5x^7}{90x^5} = \frac{5}{90} \cdot x^{7-5} = \frac{1}{18}x^2 = \frac{x^2}{18}$

Answer:

$\frac{x^2}{18}$ (matches the first option)