Question

I need help please can someone help

Answer 1

x = 8

Explanation:

`\sqrt{(896z^(15))/(225z^6)}=(xz^4)/(15)√(14z)\\\\\sqrt{(896z^(15))/(225z^6)}\qquad\text{use}\ (a^m)/(a^n)=a^(m-n)\\\\=\sqrt{((64)(14)z^(15-6))/(225)}\qquad\text{use}\ √(ab)=√(a)\cdot√(b),\ \sqrt{(a)/(b)}=(√(a))/(√(b))\\\\=(√(64)\cdot√(14)\cdot√(z^9))/(√(225))=\frac{8\cdot√(14)\cdot\sqrt{z^(8+1)}}{15}\qquad\text{use}\ a^na^m=a^(n+m)\\\\=(8√(14)\cdot√(z^8z))/(15)\qquad\text{use}\ √(ab)=√(a)\cdot√(b)`

`=(8√(14)\cdot√(z^8)\cdot√(z))/(15)=\frac{8√(14)\cdot\sqrt{z^(4\cdot2)}\cdot√(z)}{15}\qquad\text{use}\ (a^n)^m=a^(nm)\\\\=(8√(14)\cdot√((z^4)^2)\cdot√(z))/(15)\qquad\text{use}\ (√(a))^2=a\\\\=(8√(14)\cdot z^4\cdot√(z))/(15)=(8z^4√(14)\cdot√(z))/(15)\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=(8z^4√(14z))/(15)`

`(8z^4√(14z))/(15)=(xz^4√(14z))/(15)\iff x=8`