In this discussion, you will simplify and compare equivalent expressions written

Question

In this discussion, you will simplify and compare equivalent expressions written both in radical form and with rational (fractional) exponents For the factoring problem, be sure you show all steps to the factoring and solving. Show a check of your solutions back into the original equation. For the Quadratic Formula problem, be sure that you use readable notation while you are working the computational steps. Refer to Inserting Math Symbols for guidance with formatting. Present your final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required. Incorporate the following four math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): Quadratic formula Factoring Completing the square Discriminant

Explanation / Answer

1) 27^ (-2/3)

= [27^ (1/3)] ^(-2)

= [(3^3)^(1/3) ]^(-2)

= [3^(3* 1/3)]^(-2)

= [3^ 1]^(-2)

= 3^(-2)

= 1/ 3^2

= 1/9

2) (27)^ (-1/3)

= [3^3 ]^(-1/3)

= 3^[ 3* (-1/3)]

= 3^ (-1)

= 1/ 3^1

=1/3

3) [a^(1/2) b]^(1/2) * [ a *b^(1/2)]

[a^(1/2)]^(1/2) * b^(1/2) *a *b^(1/2)

= a^(1/4)*a * b^(1/2) *b^(1/2)

=a^ [ (1/4) +1] * b^[(1/2)+(1/2)]

= a^(5/4) b

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