Evaluate :
xa−b×xb−c×xc−a\sqrt{x^{a-b}} \times \sqrt{x^{b-c}} \times \sqrt{x^{c-a}}xa−b×xb−c×xc−a
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xa−b×xb−c×xc−a⇒xa−b2×xb−c2×xc−a2⇒xa−b2+b−c2+c−a2⇒xa−b+(b−c)+(c−a)2⇒xa−b+b−c+c−a2⇒x0⇒1\sqrt{x^{a-b}} \times \sqrt{x^{b-c}} \times \sqrt{x^{c-a}}\\[1em] \Rightarrow x^{\frac{a-b}{2}} \times x^{\frac{b-c}{2}} \times x^{\frac{c-a}{2}}\\[1em] \Rightarrow x^{\frac{a-b}{2} + \frac{b-c}{2} + \frac{c-a}{2}}\\[1em] \Rightarrow x^{\frac{a-b + (b-c) + (c-a)}{2}}\\[1em] \Rightarrow x^{\frac{a-b + b-c + c-a}{2}}\\[1em] \Rightarrow x^0\\[1em] \Rightarrow 1xa−b×xb−c×xc−a⇒x2a−b×x2b−c×x2c−a⇒x2a−b+2b−c+2c−a⇒x2a−b+(b−c)+(c−a)⇒x2a−b+b−c+c−a⇒x0⇒1
Hence, xa−b×xb−c×xc−a\sqrt{x^{a-b}} \times \sqrt{x^{b-c}} \times \sqrt{x^{c-a}}xa−b×xb−c×xc−a = 1
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Solve for x :
320+23=(0.6)2−3x\sqrt{32^0+\dfrac{2}{3}} = (0.6)^{2-3x}320+32=(0.6)2−3x.
Solve :
{(625−12)−14}2=(0.2)4−3x\Big{\Big(625^{-\dfrac{1}{2}}\Big)^{-\dfrac{1}{4}}\Big}^2 = (0.2)^{4-3x}{(625−21)−41}2=(0.2)4−3x
Simplify:
(x+1y)a(x−1y)b(y+1x)a(y−1x)b\dfrac{\Big(x+\dfrac{1}{y}\Big)^a\Big(x-\dfrac{1}{y}\Big)^b}{\Big(y+\dfrac{1}{x}\Big)^a\Big(y-\dfrac{1}{x}\Big)^b}(y+x1)a(y−x1)b(x+y1)a(x−y1)b
Solve for m :
1527 ÷ 152 = 15-2 x 155m + 2
