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mixer [17]
2 years ago
15

For what value of x is sq 896z^15/225z^6 = xz^4/15

Mathematics
1 answer:
Ratling [72]2 years ago
5 0

Answer:

Value of x is, 8

Step-by-step explanation:

Given:  \sqrt{\frac{896z^{15}}{225z^6}} =\frac{xz^4}{15} \sqrt{14z} ,.....[1]

To find the value of x:

Using exponent rules:

  • (a^n)^m = a^{nm}
  • a^n \cdot a^m = a^{n+m}

Taking square both sides in [1] we have;

\frac{896z^{15}}{225z^6} = (\frac{xz^4}{15})^2 \cdot (14z)

Simplify:

\frac{896z^{15}}{225z^6} =\frac{x^2z^8}{225} \cdot (14z)

or

\frac{896z^{15}}{225z^6} =\frac{14x^2z^9}{225}

Multiply both sides by \frac{225}{14z^9} we get;

x^2 = \frac{896 z^{15}}{225z^6} \times \frac{225}{14 z^9} = \frac{896 z^{15}}{14 z^{9+6}}

Simplify:

x^2 = \frac{896 z^{15}}{14 z^{15}} = 64

or

x = \sqrt{64}

Simplify:

x = 8

Therefore, the value of x is, 8


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