Question

What is the simplified form of sqaure root 72x to the power 16 over 50x 36 assume x = 0

1)6 over 5x power of 10
2)6 over 5x to power of 2
3)6 over 5x to the power of 10
4)6 over 5x to the power of 2​

Answer 1

`\large\boxed{(6)/(5x^(10))}`

Explanation:

`\sqrt{(72x^(16))/(50x^(36))}\qquad\text{simplify}\\\\=\sqrt{\frac{36x^(16)}{25x{^(20+16)}}}\qquad\text{use}\ (a^n)(a^m)=a^(n+m)\\\\=\sqrt{(36x^(16))/(25x^(20)x^(16))}\qquad\text{cancel}\ x^(16)\\\\=\sqrt{(36)/(25x^(20))}\qquad\text{use}\ \sqrt{(a)/(b)}=(√(a))/(√(b))\ \text{and}\ √(ab)=√(a)\cdot√(b)\\\\=\frac{√(36)}{√(25)\cdot\sqrt{x^(10\cdot2)}}\qquad\text{use}\ (a^n)^m=a^(nm)\\\\=\frac{6}{5\sqrt{(x^(10))^2}}\qquad\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=(6)/(5x^(10))`