Choose the correct simplification of x to the 3rd power over y to the 5th power all raised to the 2nd power.
x to the 5th power over y to the 7th power
x over y to the 3rd power
x to the 6th power over y to the 10th power
x6y10

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 =

y to the 5th power=

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

Now applying identity,

Using identity,

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

Therefore, Option 3 is correct.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.