Question

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

Answer 1

Solution:

Given => a = 2, b = a² and c = b²​

To simplify => (a/b)²×(b/c)³×(c/a)⁴

$( \frac{a}{b} )^{2} * ( \frac{b}{c} )^{3} * ( \frac{c}{a} )^{4}$

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

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

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

Put values of b and c

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

$b^{2}$

Put value of b

$(a^{2})^{2}$

Put value of a

$(2^{2})^{2}$

$(4)^{2}$

$16$

Simplification means to make the mathematical expression easier which gives us a direct answer.

Mathematical expressions can be made more hard by adding multiple brackets, numbers, constants and arithmetic expressions.

Answer 2

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

To find : Simplify  (a/b)²×(b/c)³×(c/a)⁴

Solution:

(a/b)²×(b/c)³×(c/a)⁴

= (a² * b³  * c⁴)/(b² * c³  * a⁴)

= ( b * c) / a²

b=a²

= (a² * c)/ a²

= c

c = b²

= b²

= (a²)²

= (2²)²

= 4²

= 16

a = 2

b = a² = 2² = 4

c = b² = 4² = 16

(a/b)²×(b/c)³×(c/a)⁴ = 16

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