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:
