Simplify: $x^{a + b} x^{b + c} x^{c + a}$

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Solution

$x^{a + b} x^{b + c} x^{c + a} = x^{a + b + b + c + c + a} = x^{2 (a + b + c)}$

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Similar questions

Q. Simplify:

(i)

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

(ii)

l m \sqrt{\frac{x^{l}}{x^{m}}} \times m n \sqrt{\frac{x^{m}}{x^{n}}} \times n l \sqrt{\frac{x^{n}}{x^{l}}}

Simplify: $(i) {(\frac{x^{a + b}}{x^{c}})}^{a - b} {(\frac{x^{b + c}}{x^{a}})}^{b - c} {(\frac{x^{c + a}}{x^{b}})}^{c - a} (i i) \sqrt[l m]{\frac{x^{l}}{x^{m}}} \times \sqrt[m n]{\frac{x^{m}}{x^{n}}} \times \sqrt[n l]{\frac{x^{n}}{x^{l}}}$

Q. Show that:
(i)

\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1

(ii)

{[\{\frac{x^{a (a - b)}}{x^{a (a + b)}}\} \div \{\frac{x^{b (b - a)}}{x^{b (b + a)}}\}]}^{a + b} = 1

(iii)

{(x^{\frac{1}{a - b}})}^{\frac{1}{a - c}} {(x^{\frac{1}{b - c}})}^{\frac{1}{b - a}} {(x^{\frac{1}{c - a}})}^{\frac{1}{c - b}} = 1

(iv)

{(\frac{x^{a^{2} + b^{2}}}{x^{a b}})}^{a + b} {(\frac{x^{b^{2} + c^{2}}}{x^{b c}})}^{b + c} {(\frac{x^{c^{2} + a^{2}}}{x^{a c}})}^{a + c} = x^{2 (a^{3} + b^{3} + c^{3})}

(v)

{(x^{a - b})}^{a + b} {(x^{b - c})}^{b + c} {(x^{c - a})}^{c + a} = 1

(vi)

{\{{(x^{a - a^{- 1}})}^{\frac{1}{a - 1}}\}}^{\frac{a}{a + 1}} = x

(vii)

{(\frac{a^{x + 1}}{a^{y + 1}})}^{x + y} {(\frac{a^{y + 2}}{a^{z + 2}})}^{y + z} {(\frac{a^{z + 3}}{a^{x + 3}})}^{z + x} = 1

(viii)

{(\frac{3^{a}}{3^{b}})}^{a + b} {(\frac{3^{b}}{3^{c}})}^{b + c} {(\frac{3^{c}}{3^{a}})}^{c + a} = 1

Q. Simplify

\frac{x^{a}}{x^{b}} \times \frac{x^{b}}{x^{a}} \times \frac{x^{a}}{x^{b}}

Q. Simplify

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

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Simplify: xa+bxb+cxc+a

xa+bxb+cxc+a=xa+b+b+c+c+a=x2(a+b+c)

Simplify: $x^{a + b} x^{b + c} x^{c + a}$

$x^{a + b} x^{b + c} x^{c + a} = x^{a + b + b + c + c + a} = x^{2 (a + b + c)}$