Question

1. $\frac{9(x^{5})^{3}}{3x^{9}cdot x^{2}} =$
2. $\frac{55(x^{5})^{3}cdot y^{8}}{11x^{7}cdot (y^{3})^{2}} =$

Explanation:

Step1: Simplify numerator exponent

$(x^5)^3 = x^{5\times3} = x^{15}$

Step2: Simplify denominator exponents

$3x^9 \cdot x^2 = 3x^{9+2} = 3x^{11}$

Step3: Simplify coefficients and variables

$\frac{9x^{15}}{3x^{11}} = \frac{9}{3} \cdot x^{15-11} = 3x^4$

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Step1: Simplify numerator exponents

$(x^5)^3 = x^{5\times3}=x^{15}$; numerator: $55x^{15}y^8$

Step2: Simplify denominator exponents

$(y^3)^2 = y^{3\times2}=y^6$; denominator: $11x^7y^6$

Step3: Simplify coefficients and variables

$\frac{55x^{15}y^8}{11x^7y^6} = \frac{55}{11} \cdot x^{15-7} \cdot y^{8-6} = 5x^8y^2$

Answer:

1. $3x^4$
2. $5x^8y^2$