Question

Choose the correct simplification of x to the 3rd power over y to the 5th power all raised to the 2nd power.

Answer 1

Answer:

Option 3 - x to the 6th power over y to the 10th power

Step-by-step explanation:

Given : Expression x to the 3rd power over y to the 5th power all raised to the 2nd power.

To find : Choose the correct simplification of the expression?

Solution :

Writing the expression in value form,

x to the 3rd power = $x^3$

y to the 5th power= $y^5$

x to the 3rd power over y to the 5th power all raised to the 2nd power =

$(\frac{x^3}{y^5})^2$

Now applying identity,

$(\frac{x}{y})^a=\frac{x^a}{y^a}$

$=(\frac{x^3}{y^5})^2$

$=\frac{(x^3)^2}{(y^5)^2}$

Using identity, $(x^a)^b=x^{a.b}$

$=\frac{x^{3.2}}{y^{5.2}}$

$=\frac{x^{6}}{y^{10}}$

In word form, x to the 6th power over y to the 10th power.

Therefore, Option 3 is correct.

Answer 2

$\left( \cfrac{x^3}{y^5} \right)^2=\cfrac{(x^3)^2}{(y^5)^2}=\cfrac{x^{3*2}}{y^{5*2}}=\cfrac{x^{6}}{y^{10}}$