Find the value of the expression- Xa-b2- Xb-c2- Xc-a2Xa Xb Xc4- if x- 2- a - 1- b- 2- c -3-

The correct option is C 1 (X^a+b)^2× (X^b+c)^2× (X^c+a)^2(X^aX^bX^c)^4 #160; =(2^1+2)^2× (2^2+3)^2× (2^3+1)^2(2^12^22^3)^4 ⇒ #160; ...

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Byju's Answer

Standard VII

Mathematics

Quotient Law

Find the valu...

Question

Find the value of the expression: $\frac{(X^{a + b})^{2} \times (X^{b + c})^{2} \times (X^{c + a})^{2}}{(X^{a} X^{b} X^{c})^{4}}$ , if $x = 2, a = 1, b = 2, c = 3$ .

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Solution

The correct option is C $1$
$\frac{(X^{a + b})^{2} \times (X^{b + c})^{2} \times (X^{c + a})^{2}}{(X^{a} X^{b} X^{c})^{4}}$ $= \frac{(2^{1 + 2})^{2} \times (2^{2 + 3})^{2} \times (2^{3 + 1})^{2}}{(2^{1} 2^{2} 2^{3})^{4}}$

$\Rightarrow$ $\frac{2^{6} \times 2^{10} \times 2^{8}}{(2^{1 + 2 + 3})^{4}}$

$\Rightarrow$ $\frac{2^{6 + 10 + 8}}{(2^{6})^{4}}$

$\Rightarrow$ $\frac{2^{24}}{2^{24}}$

$\Rightarrow$ $1$

$∴$ $\frac{(X^{a + b})^{2} \times (X^{b + c})^{2} \times (X^{c + a})^{2}}{(X^{a} X^{b} X^{c})^{4}} = 1$

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Similar questions

Q. The value of

\frac{{(x^{a + b})}^{2} {(x^{b + c})}^{2} {(x^{c + a})}^{2}}{{(x^{a} x^{b} x^{c})}^{4}}

is equal to:

Q. Show that

\frac{{(x^{a + b})}^{2} {(x^{b + c})}^{2} {(x^{c + a})}^{2}}{{(x^{a} x^{b} x^{c})}^{4}} = 1

Prove that :

(i) ${(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \times {(\frac{x^{b}}{x^{c}})}^{b^{2} + a b + c^{2}} \times {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + a^{2}} = 1$

(ii) ${(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b} = 1$

Q. If

a = 1

b = - 1

and

c = 0

, find the value of expression

(a^{2} - b^{2}) + (c^{2} - b^{2}) + (a^{2} - c^{2})

Q. Simplify :

{(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \times {(\frac{x^{b}}{x^{c}})}^{b^{2} + b c + c^{2}} \times {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + a^{2}}

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Find the value of the expression: (Xa+b)2×(Xb+c)2×(Xc+a)2(XaXbXc)4, if x=2,a=1,b=2,c=3.

The correct option is C 1(Xa+b)2×(Xb+c)2×(Xc+a)2(XaXbXc)4 =(21+2)2×(22+3)2×(23+1)2(212223)4⇒ 26×210×28(21+2+3)4⇒ 26+10+8(26)4⇒ 224224⇒ 1∴ (Xa+b)2×(Xb+c)2×(Xc+a)2(XaXbXc)4=1

Find the value of the expression: $\frac{(X^{a + b})^{2} \times (X^{b + c})^{2} \times (X^{c + a})^{2}}{(X^{a} X^{b} X^{c})^{4}}$ , if $x = 2, a = 1, b = 2, c = 3$ .