Answer:
Value of x is, 8
Step-by-step explanation:
Given: [tex]\sqrt{\frac{896z^{15}}{225z^6}} =\frac{xz^4}{15} \sqrt{14z}[/tex] ,.....[1]
To find the value of x:
Using exponent rules:
- [tex](a^n)^m = a^{nm}[/tex]
- [tex]a^n \cdot a^m = a^{n+m}[/tex]
Taking square both sides in [1] we have;
[tex]\frac{896z^{15}}{225z^6} = (\frac{xz^4}{15})^2 \cdot (14z)[/tex]
Simplify:
[tex]\frac{896z^{15}}{225z^6} =\frac{x^2z^8}{225} \cdot (14z)[/tex]
or
[tex]\frac{896z^{15}}{225z^6} =\frac{14x^2z^9}{225}[/tex]
Multiply both sides by [tex]\frac{225}{14z^9}[/tex] we get;
[tex]x^2 = \frac{896 z^{15}}{225z^6} \times \frac{225}{14 z^9} = \frac{896 z^{15}}{14 z^{9+6}}[/tex]
Simplify:
[tex]x^2 = \frac{896 z^{15}}{14 z^{15}} = 64[/tex]
or
[tex]x = \sqrt{64}[/tex]
Simplify:
x = 8
Therefore, the value of x is, 8
