Question

Tanisha and Neal are simplifying the expression (StartFraction (x Superscript 4 Baseline) (y Superscript negative 5 Baseline) Over 3 (x squared) (y Superscript negative 3 Baseline) EndFraction) Superscript 4. They each began the same way.

Tanisha’s Work
Neal’s Work
(StartFraction (x Superscript 4 Baseline) (y Superscript negative 5 Baseline) Over 3 (x squared) (y Superscript negative 3 Baseline) EndFraction) Superscript 4 = (StartFraction (x squared) (y Superscript negative 2 Baseline) Over 3 EndFraction) Superscript 4
(StartFraction (x Superscript 4 Baseline) (y Superscript negative 5 Baseline) Over 3 (x squared) (y Superscript negative 3 Baseline) EndFraction) Superscript 4 = StartFraction (x Superscript 16 Baseline) (y Superscript negative 20 Baseline) Over (3 Superscript 4 Baseline (x Superscript 8 Baseline) (y Superscript negative 12 Baseline) EndFraction


Which statements are true about each person’s work? Check all that apply.

Answer 1

It will be 2,3,4 and 6.

Explanation:

took the test and they came out that these where the correct. Plus when looking at the work you can tell that they both are on tract and are correct. and the next steps needed to be taken.

Answer 2

You didn't the statements from which you like to know which ones are true.

But it is discovered that Neal's work is correct to the point where he stopped, but Tanisha's work has a mistake in it.

Explanation:

Tanisha and Neal want to simplify the expression :

(x^4 y^(-5)/3x²y^(-3))^4

Tanisha's approach

(x^4 y^(-5)/3x²y^(-3))^4

= (x²y^(-2)/3^4)^4

Neil's approach.

(x^4 y^(-5)/3x²y^(-3))^4

= x^(16) y^(-20)/3^4(x^8 y^(-12))

Simplifying the expression using Tanisha's approach.

(x^4 y^(-5)/3x²y^(-3))^4

= (x²y^(-2)/3)^4

= x^(2×4) y^(-2×4)/3^4

= x^8 y^(-8)/3^4

= 3^(-4) (x/y)^8

Solving using Neal's approach.

(x^4 y^(-5)/3x²y^(-3))^4

= (x^4 y^(-5))^4/(3x²y^(-3))^4

= x^(4×4) y^(-5×4) / (3^4 x^(2×4) y^(-3×4)

= x^16 y^(-20)/ 3^4 x^8 y^(-12)

= x^(16-8) y^(-20+12) 3^(0-4)

= x^8 y^(-8) 3^(-4)

= x^8/3^4 y^8

= 3^(-4) (x/y)^8

From this, we can say that straightaway Neal's is on the line. His approach is correct, so is his work.

Tanisha's approach is acceptable too, but the results in her work is questionable. There should be

(x²y^(-2)/3)^4 not (x²y^(-2)/3^4)^4, it changes everything.