What is (15^6*12^4*5^9*6^3)/(10^{11)*3^{13}*5^4} ?

The solution to (15^6*12^4*5^9*6^3)/(10^{11)*3^{13}*5^4} is 1

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simplify (15^612^45^96^3)/(10^{11)3^{13}*5^4}

simplify

\frac{1 5 ^{6} \cdot 1 2 ^{4} \cdot 5 ^{9} \cdot 6 ^{3}}{1 0 ^{11} \cdot 3 ^{13} \cdot 5 ^{4}}

1

Solution steps

\frac{1 5 ^{6} \cdot 1 2 ^{4} \cdot 5 ^{9} \cdot 6 ^{3}}{1 0 ^{11} \cdot 3 ^{13} \cdot 5 ^{4}}

\frac{5 ^{9}}{5 ^{4}} = 5^{5}

= \frac{1 5 ^{6} \cdot 1 2 ^{4} \cdot 5 ^{5} \cdot 6 ^{3}}{1 0 ^{11} \cdot 3 ^{13}}

Factor

1 5^{6} : 5^{6} \cdot 3^{6}

= \frac{5 ^{6} \cdot 3 ^{6} \cdot 1 2 ^{4} \cdot 5 ^{5} \cdot 6 ^{3}}{1 0 ^{11} \cdot 3 ^{13}}

Factor

1 0^{11} : 5^{11} \cdot 2^{11}

= \frac{5 ^{6} \cdot 3 ^{6} \cdot 1 2 ^{4} \cdot 5 ^{5} \cdot 6 ^{3}}{5 ^{11} \cdot 2 ^{11} \cdot 3 ^{13}}

\frac{5 ^{6}}{5 ^{11}} = \frac{1}{5 ^{5}}

= \frac{3 ^{6} \cdot 1 2 ^{4} \cdot 5 ^{5} \cdot 6 ^{3}}{5 ^{5} \cdot 2 ^{11} \cdot 3 ^{13}}

Cancel the common factor:

5^{5}

= \frac{3 ^{6} \cdot 1 2 ^{4} \cdot 6 ^{3}}{2 ^{11} \cdot 3 ^{13}}

\frac{3 ^{6}}{3 ^{13}} = \frac{1}{3 ^{7}}

= \frac{1 2 ^{4} \cdot 6 ^{3}}{2 ^{11} \cdot 3 ^{7}}

Factor

1 2^{4} : 2^{8} \cdot 3^{4}

= \frac{2 ^{8} \cdot 3 ^{4} \cdot 6 ^{3}}{2 ^{11} \cdot 3 ^{7}}

\frac{2 ^{8}}{2 ^{11}} = \frac{1}{2 ^{3}}

= \frac{3 ^{4} \cdot 6 ^{3}}{2 ^{3} \cdot 3 ^{7}}

\frac{3 ^{4}}{3 ^{7}} = \frac{1}{3 ^{3}}

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

Factor

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

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

Cancel the common factor:

2^{3}

= \frac{3 ^{3}}{3 ^{3}}

Apply the fraction rule:

\frac{a}{a} = 1

= 1

9 x^{2} - 24 x y + 7 y^{2}

x^{2} - x = 3

6 x^{2} - 5 x - 2 = 0

24 x^{2} + 14 x y + 2 y^{2}

2 x^{2} = 18

What is (15^6*12^4*5^9*6^3)/(10^{11)*3^{13}*5^4} ?
The solution to (15^6*12^4*5^9*6^3)/(10^{11)*3^{13}*5^4} is 1