Question

Simplify : (a/b)²×(b/c)³×(c/a)⁴ such that a=2, b=a²,c=b²​

Answer 1

$\mathfrak{dear\:user}$

$\mathfrak{question-}$$\textbf{simplify}$ $(\frac{a}{b})^2$$\times$$(\frac{b}{c})^3$$\times$$(\frac{c}{a})^4$ $\textbf{where}$ $a = 2$, $b = a^2$  $\&$  $c = b^2$

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$\mathbb{ANSWER}$

Given => $a = 2$, $b = a^2$  $\&$  $c = b^2$

To simplify => $(\frac{a}{b})^2$$\times$$(\frac{b}{c})^3$$\times$$(\frac{c}{a})^4$

$\frac{a^2}{b^2}$$\times$$\frac{b^3}{c^3}$$\times$$\frac{c^4}{a^4}$

$\frac {a^2b}{c^3}$$\times$$\frac{c^4}{a^4}$

$\frac{bc}{a^2}$

Put values of b and c

$\frac{a^2b^2}{a^2}$

$b^2$

Put value of b

$(a^2)^2$

Put value of a

$(2^2)^2$

$4^2$

$16$

 

$NOTE-$$\textsf{1)\:Simplification means to make the mathematical expression easier which gives us a direct answer.}$$\textsf{2)\:Mathematical expressions can be made more hard by adding multiple }$ $\textsf{brackets, numbers, constants and arithmetic expressions.}$

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Answer 2

Given :

• → Simplify : (a/b)² × (b/c)³ × (c/a)⁴ such that a = 2, b = a²,c = b²

Need To Find :

• → Value of (a/b)² × (b/c)³ × (c/a)⁴

Required Solution :

• → (a/b)² × (b/c)³ × (c/a)⁴
• → a²/b² × b³/c³ × c⁴/a⁴
• → a²b/c³ × c⁴/a⁴
• → bc/a²

Putting Value of B and C :

• → a²b2/a2
• → b²

Putting value of b :

• → [a²]²

Putting Value of a :

• → (a²) ²
• → (2²)²
• → (4)²
• → 4 × 4
• → 16 [ Final Answer ]

Therefore :

• → (a/b)²×(b/c)³×(c/a)⁴ = 16

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