Question

Which is the simplified form of the expression (StartFraction (x Superscript negative 3 Baseline) (y squared) Over (x Superscript 4 Baseline) (y superscript 6 Baseline) EndFraction) cubed?
StartFraction 1 Over x Superscript 4 Baseline y EndFraction
StartFraction 1 Over x Superscript 21 Baseline y Superscript 12 Baseline EndFraction
x cubed y Superscript 12
x cubed y Superscript 24

Answer 1

Answer:

Option "StartFraction 1 Over x Superscript 21 Baseline y Superscript 12 Baseline EndFraction" is correct.

Therefore the simplest form is $(\frac{(x^{-3})(y^2)}{(x^4)(y^6)})^3=\frac{1}{x^{21}.y^{12}}$

Step-by-step explanation:

Given expression is (StartFraction (x Superscript negative 3 Baseline) (y squared) Over (x Superscript 4 Baseline) (y superscript 6 Baseline) EndFraction) cubed

The given expression can be written as

$(\frac{(x^{-3})(y^2)}{(x^4)(y^6)})^3$

To find the simplest form of the given expression :

$(\frac{(x^{-3})(y^2)}{(x^4)(y^6)})^3=(\frac{x^{-3}y^2}{x^4y^6})^3$

$=(\frac{1}{x^4.x^3y^6.y^{-2}})^3$  ( using the property $a^m=\frac{1}{a^{-m}}$ )

$=(\frac{1}{x^{4+3}y^{6-2}})^3$  (using the property $a^m.a^n=a^{m+n}$ )

$=(\frac{1}{x^7y^4})^3$

$=\frac{1}{(x^7y^4)^3}$

$=\frac{1}{(x^7)^3.(y^4)^3}$ ( using the property $(a^m)^n=a^{mn}$ )

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

Therefore the simplest form is $(\frac{(x^{-3})(y^2)}{(x^4)(y^6)})^3=\frac{1}{x^{21}.y^{12}}$

Option "StartFraction 1 Over x Superscript 21 Baseline y Superscript 12 Baseline EndFraction" is correct

Answer 2

Answer:

StartFraction 1 Over x Superscript 21 Baseline y Superscript 12 Baseline EndFraction (aka B)

Step-by-step explanation: