What is (1/81)^{x-2}(sqrt(27))^x ?

The solution to (1/81)^{x-2}(sqrt(27))^x is 3^{(-5x+16)/2}

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simplify (1/81)^{x-2}(sqrt(27))^x

simplify

(\frac{1}{81})^{x - 2} (27)^{x}

3^{\frac{- 5 x + 16}{2}}

Solution steps

(\frac{1}{81})^{x - 2} (27)^{x}

Apply exponent rule:

a^{n} b^{n} = (a \cdot b)^{n}

(27)^{x} = (27)^{x}

= (\frac{1}{81})^{x - 2} (27)^{x}

27 = 33

= (\frac{1}{81})^{x - 2} (33)^{x}

Simplify

(33)^{x} : 3^{\frac{3 x}{2}}

= (\frac{1}{81})^{x - 2} \cdot 3^{\frac{3 x}{2}}

Simplify

(\frac{1}{81})^{x - 2} : 3^{- 4 (x - 2)}

= 3^{- 4 (x - 2)} \cdot 3^{\frac{3 x}{2}}

Apply exponent rule:

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

3^{- 4 (x - 2)} \cdot 3^{\frac{3 x}{2}} = 3^{- 4 (x - 2) + \frac{3 x}{2}}

= 3^{- 4 (x - 2) + \frac{3 x}{2}}

Simplify

- 4 (x - 2) + \frac{3 x}{2} : \frac{- 5 x + 16}{2}

= 3^{\frac{- 5 x + 16}{2}}

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What is (1/81)^{x-2}(sqrt(27))^x ?
The solution to (1/81)^{x-2}(sqrt(27))^x is 3^{(-5x+16)/2}