Question

question
express in simplest radical form.
\\(\sqrt3{1512x^7y^5}\\)

Explanation:

Step1: Factor 1512 into cube factors

$1512 = 8 \times 189 = 8 \times 27 \times 7 = 2^3 \times 3^3 \times 7$

Step2: Rewrite exponents for $x$ and $y$

$x^7 = x^{6+1} = (x^2)^3 \times x$, $y^5 = y^{3+2} = y^3 \times y^2$

Step3: Rewrite the cube root

$\sqrt[3]{2^3 \times 3^3 \times 7 \times (x^2)^3 \times x \times y^3 \times y^2}$

Step4: Extract cube factors

$2 \times 3 \times x^2 \times y \times \sqrt[3]{7 x y^2}$

Step5: Multiply the outside constants

$6x^2y\sqrt[3]{7xy^2}$

Answer:

$6x^2y\sqrt[3]{7xy^2}$