Question

Which can be used to describe an equivalent expression for (s Superscript 6 Baseline) Superscript negative 3?


Adding the exponents will create an equivalent expression.
Dividing the exponents will create an equivalent expression.
There are three factors of StartFraction 1 Over s Superscript 6 Baseline EndFraction.
There are three factors of StartFraction 1 Over s Superscript 3 Baseline EndFraction.

Answer 1

Given : (s^6)^-3

(s⁶)⁻³

To Find : Which can be used to describe an equivalent expression for (s^6)^-3

Adding the exponents will create an equivalent expression.

Dividing the exponents will create an equivalent expression.

There are three factors of 1/s^6.

There are three factors of 1/s^3.

Solution

(s⁶)⁻³   = s⁻¹⁸   ( ∵ (xᵃ)ᵇ = xᵃᵇ )

(s⁶)⁻³  = (s⁻⁶)³    ( 6 * - 3 = -6 * 3 = - 18)

s⁻⁶  = 1/s⁶      ( ∵  x⁻ᵃ = 1/xᵃ)

(s⁶)⁻³ = ( 1/s⁶)³  

( 1/s⁶)³  =   ( 1/s⁶) ( 1/s⁶) ( 1/s⁶)

 Hence  three factors of 1/s⁶.

Adding the exponents  => (s⁶)⁻³ = s⁻³   ≠ s⁻¹⁸

Dividing the exponents  => (s⁶)⁻³ = s⁻²   ≠ s⁻¹⁸

There are three factors of 1/s^6.  - CORRECT OPTION

There are three factors of 1/s^3. = (1/s³)(1/s³) (1/s³)  = 1/s⁹  = s⁻⁹ ≠ s⁻¹⁸

Hence There are three factors of   1/s⁶  is equivalent expression for (s⁶)⁻³

Learn More:

Simplify 15+(3+10)×2-12of2​ - Brainly.in

brainly.in/question/23102899

2. Simplify the following using multiplication and division properties ...

brainly.in/question/11224537