What is ((15^330^218^2))/((9^312^45^6)) ?

The solution to ((15^330^218^2))/((9^312^45^6)) is 1/240

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simplify ((15^330^218^2))/((9^312^45^6))

Solution

simplify

\frac{( 1 5 ^{3} 3 0 ^{2} 1 8 ^{2} )}{( 9 ^{3} 1 2 ^{4} 5 ^{6} )}

Solution

\frac{1}{240}

Decimal Notation

0.00416 \dots

Solution steps

\frac{1 5 ^{3} \cdot 3 0 ^{2} \cdot 1 8 ^{2}}{9 ^{3} \cdot 1 2 ^{4} \cdot 5 ^{6}}

Factor

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

1 5^{3}

Factor the number:

15 = 3 \cdot 5

= (3 \cdot 5)^{3}

Apply exponent rule:

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

(3 \cdot 5)^{3} = 3^{3} \cdot 5^{3}

= 3^{3} \cdot 5^{3}

= \frac{3 ^{3} \cdot 5 ^{3} \cdot 3 0 ^{2} \cdot 1 8 ^{2}}{9 ^{3} \cdot 1 2 ^{4} \cdot 5 ^{6}}

Factor

9^{3} : 3^{6}

9^{3}

Factor the number:

9 = 3^{2}

= (3^{2})^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3^{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= 3^{6}

= \frac{3 ^{3} \cdot 5 ^{3} \cdot 3 0 ^{2} \cdot 1 8 ^{2}}{3 ^{6} \cdot 1 2 ^{4} \cdot 5 ^{6}}

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

\frac{3 ^{3}}{3 ^{6}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

= \frac{1}{3 ^{6 - 3}}

Subtract the numbers:

6 - 3 = 3

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

= \frac{5 ^{3} \cdot 3 0 ^{2} \cdot 1 8 ^{2}}{3 ^{3} \cdot 1 2 ^{4} \cdot 5 ^{6}}

\frac{5 ^{3}}{5 ^{6}} = \frac{1}{5 ^{3}}

\frac{5 ^{3}}{5 ^{6}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

= \frac{1}{5 ^{6 - 3}}

Subtract the numbers:

6 - 3 = 3

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

= \frac{3 0 ^{2} \cdot 1 8 ^{2}}{3 ^{3} \cdot 1 2 ^{4} \cdot 5 ^{3}}

Factor

3 0^{2} : 3^{2} \cdot 1 0^{2}

3 0^{2}

Factor the number:

30 = 3 \cdot 10

= (3 \cdot 10)^{2}

Apply exponent rule:

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

(3 \cdot 10)^{2} = 3^{2} \cdot 1 0^{2}

= 3^{2} \cdot 1 0^{2}

= \frac{3 ^{2} \cdot 1 0 ^{2} \cdot 1 8 ^{2}}{3 ^{3} \cdot 1 2 ^{4} \cdot 5 ^{3}}

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

\frac{3 ^{2}}{3 ^{3}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

= \frac{1}{3 ^{3 - 2}}

Subtract the numbers:

3 - 2 = 1

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

Apply exponent rule:

a^{1} = a

3^{1} = 3

= \frac{1}{3}

= \frac{1 0 ^{2} \cdot 1 8 ^{2}}{3 \cdot 1 2 ^{4} \cdot 5 ^{3}}

Factor

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

1 0^{2}

Factor the number:

10 = 2 \cdot 5

= (2 \cdot 5)^{2}

Apply exponent rule:

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

(2 \cdot 5)^{2} = 2^{2} \cdot 5^{2}

= 2^{2} \cdot 5^{2}

= \frac{2 ^{2} \cdot 5 ^{2} \cdot 1 8 ^{2}}{3 \cdot 1 2 ^{4} \cdot 5 ^{3}}

Factor

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

1 2^{4}

Factor

12 : 2^{2} \cdot 3

12

Factor the number:

12 = 4 \cdot 3

= 4 \cdot 3

Factor the number:

4 = 2^{2}

= 2^{2} \cdot 3

= (2^{2} \cdot 3)^{4}

Apply exponent rule:

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

(2^{2} \cdot 3)^{4} = (2^{2})^{4} \cdot 3^{4}

= (2^{2})^{4} \cdot 3^{4}

(2^{2})^{4} = 2^{8}

(2^{2})^{4}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 2^{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= 2^{8}

= 2^{8} \cdot 3^{4}

= \frac{2 ^{2} \cdot 5 ^{2} \cdot 1 8 ^{2}}{3 \cdot 2 ^{8} \cdot 3 ^{4} \cdot 5 ^{3}}

\frac{2 ^{2}}{2 ^{8}} = \frac{1}{2 ^{6}}

\frac{2 ^{2}}{2 ^{8}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

= \frac{1}{2 ^{8 - 2}}

Subtract the numbers:

8 - 2 = 6

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

= \frac{5 ^{2} \cdot 1 8 ^{2}}{3 \cdot 2 ^{6} \cdot 3 ^{4} \cdot 5 ^{3}}

\frac{5 ^{2}}{5 ^{3}} = \frac{1}{5}

\frac{5 ^{2}}{5 ^{3}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

= \frac{1}{5 ^{3 - 2}}

Subtract the numbers:

3 - 2 = 1

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

Apply exponent rule:

a^{1} = a

5^{1} = 5

= \frac{1}{5}

= \frac{1 8 ^{2}}{3 \cdot 2 ^{6} \cdot 3 ^{4} \cdot 5}

Factor

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

1 8^{2}

Factor

18 : 3^{2} \cdot 2

18

Factor the number:

18 = 9 \cdot 2

= 9 \cdot 2

Factor the number:

9 = 3^{2}

= 3^{2} \cdot 2

= (3^{2} \cdot 2)^{2}

Apply exponent rule:

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

(3^{2} \cdot 2)^{2} = (3^{2})^{2} \cdot 2^{2}

= (3^{2})^{2} \cdot 2^{2}

(3^{2})^{2} = 3^{4}

(3^{2})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3^{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= 3^{4}

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

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

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

\frac{3 ^{4}}{3}

Apply exponent rule:

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

= 3^{4 - 1}

Subtract the numbers:

4 - 1 = 3

= 3^{3}

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

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

\frac{3 ^{3}}{3 ^{4}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

Subtract the numbers:

4 - 3 = 1

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

Apply exponent rule:

a^{1} = a

3^{1} = 3

= \frac{1}{3}

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

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

\frac{2 ^{2}}{2 ^{6}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

= \frac{1}{2 ^{6 - 2}}

Subtract the numbers:

6 - 2 = 4

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

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

\frac{1}{2 ^{4} \cdot 3 \cdot 5} = \frac{1}{240}

\frac{1}{2 ^{4} \cdot 3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{1}{2 ^{4} \cdot 15}

2^{4} \cdot 15 = 240

2^{4} \cdot 15

2^{4} = 16

= 16 \cdot 15

Multiply the numbers:

16 \cdot 15 = 240

= 240

= \frac{1}{240}

= \frac{1}{240}

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Frequently Asked Questions (FAQ)

What is ((15^330^218^2))/((9^312^45^6)) ?
The solution to ((15^330^218^2))/((9^312^45^6)) is 1/240