Question

98 points! Easy! Show work! PART 2!

Answer 1

Answer:

14) The perimeter of this square is given as 28a²b⁴

The perimeter formula of a square is P = 4 x side

28a²b⁴ = 4s

\frac{28a^2b^4}{4} = \frac{4s}{4}

7a²b⁴ = s

Area formula of a square is:

A = side²

  = ( 7a²b⁴)²

  = 49a⁴b⁸

15)  \frac{(r^2st^3)(20r^-^3s^-^1t^-^4)}{(-4r^-^2t)^3}

Let's deal with it one by one and combine at the end

Numerator = ( r²st³ )( 20r⁻³s⁻¹t⁻⁴ )

The product of power rule applies here

                  = ( 20r⁻¹t⁻¹ ) → { r²⁺⁽⁻³⁾s¹⁻¹t³⁺⁽⁻⁴⁾ }

Denominator = ( -4r⁻²t )³

The power of a product rule applies here

                      = ( -64r⁻⁶t³ ) → ((-4)³(r⁻²ˣ³)(t)³)

Combine =  \frac{20r^-^1t^-^1}{-64r^-^6t^3}

Quotient of powers rule apply here

Lets separate again: \frac{r^6}{r} = r^5 ,  \frac{1}{t^3(t)} = \frac{1}{t^4}

Final =  \frac{20r^5}{-64t^4} = -\frac{5r^5}{16t^4}

16)  \sqrt[3]{x^4}

The power inside the root will be the numerator and root number will be the denominator

x^ \frac{4}{3}

17)  k^\frac{3}{4} ×  k^\frac{1}{2} = k^ \frac{3}{8}

The numerator will be the power inside and the denominator will be the root number

\sqrt[8]{x^3}

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Step-by-step explanation:

Answer 2

Hey there :)

14) The perimeter of this square is given as 28a²b⁴ 
The perimeter formula of a square is P = 4 x side
28a²b⁴ = 4s
$\frac{28a^2b^4}{4} = \frac{4s}{4}$
7a²b⁴ = s

Area formula of a square is:
A = side²
   = ( 7a²b⁴)²
   = 49a⁴b⁸

15) $\frac{(r^2st^3)(20r^-^3s^-^1t^-^4)}{(-4r^-^2t)^3}$
Let's deal with it one by one and combine at the end

Numerator = ( r²st³ )( 20r⁻³s⁻¹t⁻⁴ )
The product of power rule applies here
                   = ( 20r⁻¹t⁻¹ ) → { r²⁺⁽⁻³⁾s¹⁻¹t³⁺⁽⁻⁴⁾ }
 
Denominator = ( -4r⁻²t )³
The power of a product rule applies here
                       = ( -64r⁻⁶t³ ) → ((-4)³(r⁻²ˣ³)(t)³)

Combine = $\frac{20r^-^1t^-^1}{-64r^-^6t^3}$
Quotient of powers rule apply here 

Lets separate again: $\frac{r^6}{r} = r^5$ , $\frac{1}{t^3(t)} = \frac{1}{t^4}$

Final = $\frac{20r^5}{-64t^4} = -\frac{5r^5}{16t^4}$

16) $\sqrt[3]{x^4}$
The power inside the root will be the numerator and root number will be the denominator 

$x^ \frac{4}{3}$

17) $k^\frac{3}{4}$× $k^\frac{1}{2} = k^ \frac{3}{8}$

The numerator will be the power inside and the denominator will be the root number

$\sqrt[8]{x^3}$