Question

Choose the correct simplification of x to the 12th power times z to the 11th power all over x to the 2nd power times z to the 4th power. x10z7 x14z15 1 over x to the 10th power times z to the 7th power 1 over x to the 14th power times z to the 15th power

Answer 1

Answer:

The option A) $x^{10}z^7$ is correct answer.

The correct simplification for the given expression $\frac{x^{12}\times z^{11}}{x^2\times z^4}$ is $x^{10}z^7$

Step-by-step explanation:

Given expression is x to the 12th power times z to the 11th power all over x to the 2nd power times z to the 4th power.

The given expression can be written as $\frac{x^{12}\times z^{11}}{x^2\times z^4}$

To choose the correct simplification of the given expression :

Now we have to simplify the given expression as below

$\frac{x^{12}\times z^{11}}{x^2\times z^4}$

$=x^{12}\times z^{11}(x^{-2}\times z^{-4})$   ( by using the identity $\frac{1}{a^m}=a^{-m}$ )

$=(x^{12}.x^{-2})\times (z^{11}.z^{-4})$

$=x^{12-2}\times z^{11-4}$ ( by using the identity $a^m.a^n=a^{m+n}$ )

$=x^{10}\times z^7$

$=x^{10}z^7$

∴ $\frac{x^{12}\times z^{11}}{x^2\times z^4}=x^{10}z^7$

The correct simplification for the given expression $\frac{x^{12}\times z^{11}}{x^2\times z^4}$ is $x^{10}z^7$

Hence option A) $x^{10}z^7$ is correct answer.