Question

find the values of a, b and c in the equation below (x^5yz^4)^3/x^3yz= x^a y^b z^c

Answer 1

Answer: a = 12, b = 2, c = 11

Step-by-step explanation:

Using exponent rules we can distribute the exponent of 3 to the xyz.

This results in the numerator now being. $x^{5*3}+y^{1*3}+z^{4*3}$ This can be simplified to, $x^{15}y^{3}z^{12}$.

Now divide the numerator by the denominator subtracting the exponents.

Which equals, $x^{12}y^{2}z^{11}$

So a = 12

b = 2

and

c = 11

Answer 2

The values of $a, \ b,\ c$ are  $12,\ 2,\ 11$ .

What are exponent ?

Exponent indicates that the base is to be raised to a certain power. So, it is the power of the base.

We have,

$\frac{(x^5yz^4)^3}{x^3yz}=x^ay^bz^c$

Now simplify the above given equation;

$\frac{(x^5*3y^1*3z^4*3)}{x^3yz}=x^ay^bz^c$

$\frac{(x^{15}y^3z^{12})}{x^3yz}=x^ay^bz^c$

Now, Using the exponent rule;

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

So,

$(x^{15-3}y^{3-1}z^{12-1})=x^ay^bz^c$

$(x^{12}y^{2}z^{11})=x^ay^bz^c$

Now,

As we see variables on both sides of equation are same (i.e. bases of powers are same), so now compare the powers of sides of variables;

⇒    $x^{12}=x^a$

       $a=12$,

And, $y^2=y^b$

         $b=2$

And, $z^{11}=z^c$

         $c=11$

So, the values of $a, \ b,\ c$ are $12,\ 2,\ 11$ which are find out using the  exponent rule.

Hence, we can say that the values of $a, \ b,\ c$ are $12,\ 2,\ 11$ .

To know more about exponent click here

https://brainly.com/question/5497425

#SPJ3