Question

Which is the simplified form of the expression

Answer 1

Answer:

B) $\frac{1}{x^{21} y^{12} }$

Step-by-step explanation:

The given expression is $(\frac{(x^{-3} (y^{2}) }{x^4 y^6} )^3$

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

= $\frac{x^{-9}(y^6) }{x^{12}y^{18} }$

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

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

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

= $\frac{1}{x^{21} y^{12} }$

Therefore the answer is B) $\frac{1}{x^{21} y^{12} }$

Answer 2

Answer:

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

Step-by-step 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)