What is 3^x-3^{x-1}-3^{x-2} ?

The solution to 3^x-3^{x-1}-3^{x-2} is 5*3^{x-2}

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simplify 3^x-3^{x-1}-3^{x-2}

simplify

3^{x} - 3^{x - 1} - 3^{x - 2}

5 \cdot 3^{x - 2}

Solution steps

3^{x} - 3^{x - 1} - 3^{x - 2}

3^{x} = 3^{x - 2 + 2}, 3^{x - 1} = 3^{x - 2 + 1}

= 3^{x - 2 + 2} - 3^{x - 2 + 1} - 3^{x - 2}

Apply exponent rule:

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

3^{x - 2 + 2} = 3^{2} \cdot 3^{x - 2}, 3^{x - 2 + 1} = 3^{1} \cdot 3^{x - 2}

= 3^{2} \cdot 3^{x - 2} - 3^{1} \cdot 3^{x - 2} - 3^{x - 2}

Factor out common term

3^{x - 2}

= 3^{x - 2} (3^{2} - 3^{1} - 1)

Refine

= 5 \cdot 3^{x - 2}

(2 x + 3 z)^{3}

81 y^{4} - 625

125 x^{3} + 64 y^{3}

a (- a)^{3}

(v) \cdot (2 x^{2} + 3)^{\frac{5}{3}} \cdot (x + 5)^{\frac{- 1}{2}}