What is (2pi)^2(2\times 10^{-2}) ?

The solution to (2pi)^2(2\times 10^{-2}) is (2pi^2)/(25)

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simplify (2pi)^2(2\times 10^{-2})

simplify

(2 π)^{2} (2 \cdot 1 0^{- 2})

\frac{2 π ^{2}}{25}

Decimal Notation

0.78956 \dots

Solution steps

(2 π)^{2} (2 \cdot 1 0^{- 2})

Apply exponent rule:

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

= 2 \cdot \frac{1}{1 0 ^{2}} (2 π)^{2}

(2 π)^{2} = 2^{2} π^{2}

= 2^{2} \cdot 2 π^{2} \frac{1}{1 0 ^{2}}

Apply exponent rule:

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

2^{2} \cdot 2 = 2^{2 + 1}

= π^{2} \cdot 2^{2 + 1} \cdot \frac{1}{1 0 ^{2}}

Add the numbers:

2 + 1 = 3

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

Multiply fractions:

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

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

Multiply:

1 \cdot π^{2} = π^{2}

= \frac{2 ^{3} π ^{2}}{1 0 ^{2}}

Factor

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

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

Cancel

\frac{π ^{2} \cdot 2 ^{3}}{2 ^{2} \cdot 5 ^{2}} : \frac{2 π ^{2}}{5 ^{2}}

= \frac{2 π ^{2}}{5 ^{2}}

5^{2} = 25

= \frac{2 π ^{2}}{25}

4 e^{4 x} \cdot e^{- x}

π \cdot 1 0^{2} \cdot 10

(3 x^{4}) (6 x^{6})

e^{- 5 \cdot 0.6}

What is (2pi)^2(2\times 10^{-2}) ?
The solution to (2pi)^2(2\times 10^{-2}) is (2pi^2)/(25)