Question

Which is the simplified form of the expression

Answer 1

B. 1/(x^21y^12)

Explanation:

First solve of x:

x^-3 / x^4 is same thing as 1/ x^3x^4 which is equal to 1/x^7

Now the cube part: (1/x^7)^3 = 1/x^21

Solve for y:

y^2 / y^6

1/ y^-2y^6 = 1/y^4

(1/y^4)^3

1/y^12

Answer: 1/(x^21y^12)

Answer 2

B)
`(1)/(x^(21) y^(12) )`

Explanation:

The given expression is
`(((x^(-3) (y^(2)) )/(x^4 y^6) )^3`

Now we can bring the power 3 inside the bracket using the rule
`(a^(m) )^n = a^(mn)`

=
`(x^(-9)(y^6) )/(x^(12)y^(18)  )`

Now we have to use the quotient rule and simplify it.

`(a^m)/(a^n) = a^(m-n)`

Using the above rule, we get

=
`x^(-9 -12) *y^(6-18)`

=
`x^(-21) *y^(-12)`

Since we have a negative exponent. We can rewrite using the rule a^-m = 1/a^m

=
`(1)/(x^(21) y^(12) )`

Therefore the answer is B)
`(1)/(x^(21) y^(12) )`