Question

a 9. Simplify: (a/b)^2 × (b/c)^3 × (c/a)^4 such that a=2, b=a^2, c=b^2​

Answer 1

Answer:

$(a/b)^2 \times (b/c)^3 \times (c/a)^4 = 1/4$

Step-by-step explanation:

Given: $(a/b)^2 \times (b/c)^3 \times (c/a)^4$

Put $a=2, b=a^2, c=b^2$​ in $(a/b)^2 \times (b/c)^3 \times (c/a)^4$

$(a/b)^2 \times (b/c)^3 \times (c/a)^4 = (\frac{a}{a^2} )^2 \times (\frac{b}{b^2} )^2 \times (\frac{b^2}{b} )^2\\= (\frac{1}{a} )^2 \times (\frac{1}{b} )^2 \times (b)^2\\= \frac{1}{a^2} \times\frac{1}{b^2} \times b^2\\= \frac{1}{a^2} \\= \frac{1}{(2)^2} \\= \frac{1}{4}$