What is (3^2)^3*(2.3^5)^{-2}*(18)^2 ?

The solution to (3^2)^3*(2.3^5)^{-2}*(18)^2 is 57.01566…

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simplify (3^2)^3(2.3^5)^{-2}(18)^2

simplify

(3^{2})^{3} \cdot (2. 3^{5})^{- 2} \cdot (18)^{2}

57.01566 \dots

Solution steps

(3^{2})^{3} (2. 3^{5})^{- 2} (18)^{2}

(3^{2})^{3} : 3^{6}

= 3^{6} (2. 3^{5})^{- 2} \cdot 1 8^{2}

(2. 3^{5})^{- 2} : 2. 3^{- 10}

= 3^{6} \cdot 2. 3^{- 10} \cdot 1 8^{2}

Factor integer

18 = 3^{2} \cdot 2

= 3^{6} \cdot 2. 3^{- 10} (3^{2} \cdot 2)^{2}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

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

= 3^{6} \cdot 2. 3^{- 10} (3^{2})^{2} \cdot 2^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

= 3^{6} \cdot 2. 3^{- 10} \cdot 3^{2 \cdot 2} \cdot 2^{2}

Refine

= 3^{6} \cdot 2. 3^{- 10} \cdot 3^{4} \cdot 2^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3^{6} \cdot 3^{4} = 3^{6 + 4}

= 2. 3^{- 10} \cdot 3^{6 + 4} \cdot 2^{2}

Add the numbers:

6 + 4 = 10

= 2. 3^{- 10} \cdot 3^{10} \cdot 2^{2}

Apply exponent rule:

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

2. 3^{- 10} = \frac{1}{2. 3 ^{10}}

= 3^{10} \cdot 2^{2} \cdot \frac{1}{2. 3 ^{10}}

Multiply fractions:

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

= \frac{1 \cdot 3 ^{10} \cdot 2 ^{2}}{2. 3 ^{10}}

Multiply:

1 \cdot 3^{10} = 3^{10}

= \frac{3 ^{10} \cdot 2 ^{2}}{2. 3 ^{10}}

3^{10} \cdot 2^{2} = 236196

= \frac{236196}{2. 3 ^{10}}

2. 3^{10} = 4142.65112 \dots

= \frac{236196}{4142.65112 \dots}

Divide the numbers:

\frac{236196}{4142.65112 \dots} = 57.01566 \dots

= 57.01566 \dots

0.0365 (0.083145 \cdot 305)^{- 2}

(e^{m + \frac{r ^{2}}{2}})^{2}

e^{- x} \cdot x e^{x}

2

What is (3^2)^3*(2.3^5)^{-2}*(18)^2 ?
The solution to (3^2)^3*(2.3^5)^{-2}*(18)^2 is 57.01566…