What is 40(5)^{-0.5}(1/(25sqrt(5)))^{0.2} ?

The solution to 40(5)^{-0.5}(1/(25sqrt(5)))^{0.2} is 8

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simplify 40(5)^{-0.5}(1/(25sqrt(5)))^{0.2}

simplify

40 (5)^{- 0.5} (\frac{1}{25 5})^{0.2}

8

Solution steps

40 (5)^{- 0.5} (\frac{1}{25 5})^{0.2}

Apply exponent rule:

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

= 40 \cdot \frac{1}{5} (\frac{1}{25 5})^{0.2}

Multiply fractions:

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

= \frac{1 \cdot 40 ( \frac{1}{25 5} ) ^{0.2}}{5}

Multiply the numbers:

1 \cdot 40 = 40

= \frac{40 ( \frac{1}{25 5} ) ^{0.2}}{5}

Factor

40 : 2^{3} \cdot 5

= \frac{2 ^{3} \cdot 5 ( \frac{1}{25 5} ) ^{0.2}}{5}

Cancel

\frac{2 ^{3} \cdot 5 ( \frac{1}{25 5} ) ^{0.2}}{5} : 2^{3} 5 (\frac{1}{25 5})^{0.2}

= 2^{3} 5 (\frac{1}{25 5})^{0.2}

2^{3} = 8

= 85 (\frac{1}{25 5})^{0.2}

5 = 2.23606 \dots

= 8 \cdot 2.23606 \dots (\frac{1}{25 5})^{0.2}

(\frac{1}{25 5})^{0.2} = 0.4472135955

= 8 \cdot 0.4472135955 \cdot 2.23606 \dots

Multiply the numbers:

8 \cdot 2.23606 \dots \cdot 0.4472135955 = 8

= 8

(5)^{65}

k^{2} (k + 2)^{2}

\frac{3 + 5}{3 - 5}

p^{2} (1 - 2 p) (1 - p)^{2}

What is 40(5)^{-0.5}(1/(25sqrt(5)))^{0.2} ?
The solution to 40(5)^{-0.5}(1/(25sqrt(5)))^{0.2} is 8