What is factor a^{x-1}b-b^{n-1}a ?

The solution to factor a^{x-1}b-b^{n-1}a is (b^2a^x-a^2b^n)/(ab)

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factor a^{x-1}b-b^{n-1}a

factor

a^{x - 1} b - b^{n - 1} a

\frac{b ^{2} a ^{x} - a ^{2} b ^{n}}{ab}

Solution steps

a^{x - 1} b - b^{n - 1} a

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= a^{- 1} b a^{x} - a b^{- 1} b^{n}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

b = b^{- 1} b^{2}, a = a^{- 1} a^{2}

= (a^{- 1} a^{2})^{x} (a^{- 1} a^{2})^{- 1} b^{- 1} b^{2} - (b^{- 1} b^{2})^{n} (b^{- 1} b^{2})^{- 1} a^{- 1} a^{2}

Factor out common term

a^{- 1} b^{- 1}

= a^{- 1} b^{- 1} (a^{x} b^{2} - b^{n} a^{2})

Refine

= \frac{- a ^{2} b ^{n} + b ^{2} a ^{x}}{ab}

- 5 x + 20 x + 2.1

6 m^{2} + 7 m^{2} - 20

+ (- \frac{1}{2})

- (+ 21)

25 x^{2} y^{1} - 121

What is factor a^{x-1}b-b^{n-1}a ?
The solution to factor a^{x-1}b-b^{n-1}a is (b^2a^x-a^2b^n)/(ab)