Prove that xab-cxba-c-xbcxac-1

x ^ a(b c) / x ^ b(a c) ÷ x ^ bc / x ^ ac = x ^ a(b c) b(a c) ÷ x ^ bc ac = x ^ ab ac ba+bc ÷ x ^ bc ac = x ^ bc ac ÷ x ^ bc ac =1 ...

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Exponents with Like Bases

Prove that ...

Question

Prove that $\frac{x^{a (b - c)}}{x^{b (a - c)}} \div (\frac{x^{b c}}{x^{a c}}) = 1$

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Solution

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

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

Find the value of $\frac{x^{a (b - c)}}{x^{b (a - c)}} \div (\frac{x^{b}}{x^{a}})^{c}$

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

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

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