What is 36^n*12^{-2n} ?

The solution to 36^n*12^{-2n} is 1/(4^n)

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simplify 36^n*12^{-2n}

simplify

3 6^{n} \cdot 1 2^{- 2 n}

\frac{1}{4 ^{n}}

Solution steps

3 6^{n} \cdot 1 2^{- 2 n}

Simplify

1 2^{- 2 n} : \frac{1}{14 4 ^{n}}

= 3 6^{n} \cdot \frac{1}{14 4 ^{n}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 6 ^{n} \cdot 1}{14 4 ^{n}}

Apply rule:

a \cdot 1 = a

3 6^{n} \cdot 1 = 3 6^{n}

= \frac{3 6 ^{n}}{14 4 ^{n}}

Factor

14 4^{n} : 3 6^{n} \cdot 4^{n}

= \frac{3 6 ^{n}}{3 6 ^{n} \cdot 4 ^{n}}

Cancel the common factor:

3 6^{n}

= \frac{1}{4 ^{n}}

10 \cdot \frac{3}{2}

\frac{60}{36}

\frac{7}{3} \div 6

x + \frac{x ^{2}}{2} + 2 x^{2} - x