What is (360^{30}*1000^{50})/(48^{60)*625^{45}} ?

The solution to (360^{30}*1000^{50})/(48^{60)*625^{45}} is 1

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simplify (360^{30}1000^{50})/(48^{60)625^{45}}

simplify

\frac{36 0 ^{30} \cdot 100 0 ^{50}}{4 8 ^{60} \cdot 62 5 ^{45}}

1

Solution steps

\frac{36 0 ^{30} \cdot 100 0 ^{50}}{4 8 ^{60} \cdot 62 5 ^{45}}

Factor

36 0^{30} : 2 4^{30} \cdot 1 5^{30}

= \frac{2 4 ^{30} \cdot 1 5 ^{30} \cdot 100 0 ^{50}}{4 8 ^{60} \cdot 62 5 ^{45}}

Factor

4 8^{60} : 2 4^{60} \cdot 2^{60}

= \frac{2 4 ^{30} \cdot 1 5 ^{30} \cdot 100 0 ^{50}}{2 4 ^{60} \cdot 2 ^{60} \cdot 62 5 ^{45}}

\frac{2 4 ^{30}}{2 4 ^{60}} = \frac{1}{2 4 ^{30}}

= \frac{1 5 ^{30} \cdot 100 0 ^{50}}{2 4 ^{30} \cdot 2 ^{60} \cdot 62 5 ^{45}}

Factor

1 5^{30} : 3^{30} \cdot 5^{30}

= \frac{3 ^{30} \cdot 5 ^{30} \cdot 100 0 ^{50}}{2 4 ^{30} \cdot 2 ^{60} \cdot 62 5 ^{45}}

Factor

2 4^{30} : 3^{30} \cdot 8^{30}

= \frac{3 ^{30} \cdot 5 ^{30} \cdot 100 0 ^{50}}{3 ^{30} \cdot 8 ^{30} \cdot 2 ^{60} \cdot 62 5 ^{45}}

Cancel the common factor:

3^{30}

= \frac{5 ^{30} \cdot 100 0 ^{50}}{8 ^{30} \cdot 2 ^{60} \cdot 62 5 ^{45}}

Factor

62 5^{45} : 5^{180}

= \frac{5 ^{30} \cdot 100 0 ^{50}}{8 ^{30} \cdot 2 ^{60} \cdot 5 ^{180}}

\frac{5 ^{30}}{5 ^{180}} = \frac{1}{5 ^{150}}

= \frac{100 0 ^{50}}{8 ^{30} \cdot 2 ^{60} \cdot 5 ^{150}}

Factor

100 0^{50} : 8^{50} \cdot 12 5^{50}

= \frac{8 ^{50} \cdot 12 5 ^{50}}{8 ^{30} \cdot 2 ^{60} \cdot 5 ^{150}}

\frac{8 ^{50}}{8 ^{30}} = 8^{20}

= \frac{8 ^{20} \cdot 12 5 ^{50}}{2 ^{60} \cdot 5 ^{150}}

Factor

8^{20} : 2^{60}

= \frac{2 ^{60} \cdot 12 5 ^{50}}{2 ^{60} \cdot 5 ^{150}}

Cancel the common factor:

2^{60}

= \frac{12 5 ^{50}}{5 ^{150}}

Factor

12 5^{50} : 5^{150}

= \frac{5 ^{150}}{5 ^{150}}

Apply the fraction rule:

\frac{a}{a} = 1

= 1

\frac{5 x - 2}{x ^{2} + 1} \leq 1

5 d^{2} - 22 d + 8 = 0

(2 i - 1)^{2} \cdot (\frac{4}{1 - i} + \frac{2 - i}{1 + i})

7 (2 x - 1) - 3 = 6 + 6 x

(\frac{3}{2}) (\frac{3}{2})

What is (360^{30}*1000^{50})/(48^{60)*625^{45}} ?
The solution to (360^{30}*1000^{50})/(48^{60)*625^{45}} is 1