Question

When 27x^2z/-3x^2z^6 is completely simplified , the exponent on the variable z is _____

Answer 1

$\bf \cfrac{27x^2z}{-3x^2z^6}\implies -\cfrac{27}{3}\cdot \cfrac{x^2z}{x^2z^6}\implies -9\cdot \cfrac{x^2x^{-2}}{z^6z^{-1}}\implies -9\cdot \cfrac{x^{2-2}}{z^{6-1}} \\\\\\ -9\cdot \cfrac{x^0}{z^5}\implies -9\cdot \cfrac{1}{z^5}\implies -\cfrac{9}{z^5}$

Answer 2

Answer:

Hence the exponent on the variable z is:

-5

Step-by-step explanation:

We have to simplify the expression:

27x^2z/-3x^2z^6

This expression is basically:

$\dfrac{27x^2z}{-3x^2z^6}$

As we know that both 3 and 27 are multiples of 3 hence, we divide both the numerator and denominator by 3 to obtain:

$\dfrac{-9x^2z}{x^2z^6}$

Also we know that:

$\dfrac{a^m}{a^n}=a^{m-n}$

Hence we could write our expression as:

$\dfrac{-9x^2z}{x^2z^6}=-9\times x^{2-2}\times z^{1-6}=-9x^0z^{-5}=-9z^{-5}=\dfrac{-9}{z^5}$

Hence the exponent on the variable z is:

-5