Simplify using the law of rational exponents?
1)³√8c^8
2)^5√-96x^25y^12
3)√40r^5t^3s^8
please answer in steps
3) $\displaystyle \sqrt{40r^5t^3s^8}=\sqrt{4 \cdot 10 \cdot r^4 \cdot r \cdot t^2 \cdot t \cdot s^8}=2r^2s^4t\sqrt{10rt}$
Using rational exponents:
$\displaystyle \sqrt{40r^5t^3s^8}=\sqrt{4 \cdot 10 \cdot r^5 \cdot t^3 \cdot s^8}=(2^2)^{1/2}\cdot 10^{1/2} \cdot r^{5/2} \cdot t^{3/2} \cdot s^{8/2}=2 \cdot 10^{1/2} \cdot r^{5/2} \cdot t^{3/2} \cdot s^4$
I'm going to guess that you mean this:
2) $\displaystyle \sqrt[5]{-96x^{25}y^{12}}=\sqrt[5]{-32 \cdot 3 \cdot x^{25} \cdot y^{12}}=-2x^5y^2\sqrt[5]{3y^2}$
Using rational exponents:
$\displaystyle \sqrt[5]{-96x^{25}y^{12}}=\sqrt[5]{-32 \cdot 3 \cdot x^{25} \cdot y^{12}}=-2 \cdot 3^{1/5}x^5y^{12/5}$