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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

If $P = \frac{96}{9597}$,$Q = \frac{97}{96 \times 98}$,and $R = \frac{1}{97}$,then which of the following is the smallest?

Write down the following quotients in descending order:
$1.$ $\frac{368.39}{17}$
$2.$ $\frac{170.50}{62}$
$3.$ $\frac{875.65}{83}$

$12.1212 + 17.0005 - 9.1102 = ?$

If $\sqrt{1+\frac{x}{144}}=\frac{13}{12},$ then $x$ equals to

$108 \div ?$ of $\frac{1}{3} + \frac{2}{5} \times 3 \frac{3}{4} = 10 \frac{1}{2}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module