What is (12^3*6^5)/(9^4*2^{10)} ?

The solution to (12^3*6^5)/(9^4*2^{10)} is 2

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simplify (12^36^5)/(9^42^{10)}

simplify

\frac{1 2 ^{3} \cdot 6 ^{5}}{9 ^{4} \cdot 2 ^{10}}

2

Solution steps

\frac{1 2 ^{3} \cdot 6 ^{5}}{9 ^{4} \cdot 2 ^{10}}

Factor

1 2^{3} : 3^{3} \cdot 4^{3}

= \frac{3 ^{3} \cdot 4 ^{3} \cdot 6 ^{5}}{9 ^{4} \cdot 2 ^{10}}

Factor

9^{4} : 3^{8}

= \frac{3 ^{3} \cdot 4 ^{3} \cdot 6 ^{5}}{3 ^{8} \cdot 2 ^{10}}

\frac{3 ^{3}}{3 ^{8}} = \frac{1}{3 ^{5}}

= \frac{4 ^{3} \cdot 6 ^{5}}{3 ^{5} \cdot 2 ^{10}}

Factor

4^{3} : 2^{6}

= \frac{2 ^{6} \cdot 6 ^{5}}{3 ^{5} \cdot 2 ^{10}}

\frac{2 ^{6}}{2 ^{10}} = \frac{1}{2 ^{4}}

= \frac{6 ^{5}}{3 ^{5} \cdot 2 ^{4}}

Factor

6^{5} : 3^{5} \cdot 2^{5}

= \frac{3 ^{5} \cdot 2 ^{5}}{3 ^{5} \cdot 2 ^{4}}

Cancel the common factor:

3^{5}

= \frac{2 ^{5}}{2 ^{4}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

= 2^{5 - 4}

Subtract the numbers:

5 - 4 = 1

= 2^{1}

Apply exponent rule:

a^{1} = a

= 2

(7 - 6 i) (3 + 2 i)

7 (- 2 y + 8)

\frac{9}{15} - \frac{3}{8}

\frac{1 - cos ^{2} ( x )}{cos ^{2} ( x )}

sec (θ) cot (θ)