Find the value of frac{(0.064-0.008)(0.16-0.0 | vedclass

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Question

(A) Given expression: $\frac{(0.064-0.008)(0.16-0.04)}{(0.16+0.08+0.04)(0.4+0.2)^{3}}$
Express the terms as powers of $0.4$ and $0.2$:
$0.064 = 0.4^

Vedclass · Accepted Answer

$\frac{1}{9}$

Vedclass · Answer

(A) Given expression: $\frac{(0.064-0.008)(0.16-0.04)}{(0.16+0.08+0.04)(0.4+0.2)^{3}}$
Express the terms as powers of $0.4$ and $0.2$:
$0.064 = 0.4^{3}$,$0.008 = 0.2^{3}$,$0.16 = 0.4^{2}$,$0.04 = 0.2^{2}$,$0.08 = 0.4 	imes 0.2$
Substitute these into the expression:
Numerator: $(0.4^{3}-0.2^{3})(0.4^{2}-0.2^{2})$
Denominator: $(0.4^{2}+0.4 	imes 0.2+0.2^{2})(0.4+0.2)^{3}$
Using algebraic identities $a^{3}-b^{3} = (a-b)(a^{2}+ab+b^{2})$ and $a^{2}-b^{2} = (a-b)(a+b)$:
Numerator: $(0.4-0.2)(0.4^{2}+0.4 	imes 0.2+0.2^{2}) 	imes (0.4-0.2)(0.4+0.2)$
Now the expression becomes:
$\frac{(0.4-0.2)(0.4^{2}+0.4 	imes 0.2+0.2^{2})(0.4-0.2)(0.4+0.2)}{(0.4^{2}+0.4 	imes 0.2+0.2^{2})(0.4+0.2)^{3}}$
Cancel the common terms $(0.4^{2}+0.4 	imes 0.2+0.2^{2})$ and one $(0.4+0.2)$:
$= \frac{(0.4-0.2)^{2}}{(0.4+0.2)^{2}} = \frac{(0.2)^{2}}{(0.6)^{2}} = \frac{0.04}{0.36} = \frac{4}{36} = \frac{1}{9}$

Find the value of $\frac{(0.064-0.008)(0.16-0.04)}{(0.16+0.08+0.04)(0.4+0.2)^{3}}$.

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