Question

Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed?

Answer 1

C

Explanation:

Answer 2

The value to the given expression is 8

Therefore
`\left[((10^4)(5^2))/((10^3)(5^3))\right]^3=8`

Explanation:

Given expression is (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed

Given expression can be written as below

`\left[((10^4)(5^2))/((10^3)(5^3))\right]^3`

To find the value of the given expression:

`\left[((10^4)(5^2))/((10^3)(5^3))\right]^3=(((10^4)(5^2))^3)/(((10^3)(5^3))^3)`

( By using the property (
`((a)/(b))^m=(a^m)/(b^m)` )

`=((10^4)^3(5^2)^3)/((10^3)^3(5^3)^3)`

( By using the property
`(ab)^m=a^mb^m` )

`=((10^(12))(5^6))/((10^9)(5^9))`

( By using the property
`(a^m)^n=a^(mn)` )

`=(10^(12))(5^6)(10^(-9))(5^(-9))`

( By using the property
`(1)/(a^m)=a^(-m)` )

`=(10^(12-9))(5^(6-9))` (By using the property
`a^m.b^n=a^(m+n)` )

`=(10^3)(5^(-3))`

`=(10^3)/(5^3)` ( By using the property
`a^(-m)=(1)/(a^m)` )

`=(1000)/(125)`

`=8`

Therefore
`\left[((10^4)(5^2))/((10^3)(5^3))\right]^3=8`

Therefore the value to the given expression is 8