What is (1.6*10^{-19})^2 ?

The solution to (1.6*10^{-19})^2 is 1/(25*2^{32)*5^{38}}

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simplify (1.6*10^{-19})^2

simplify

(1.6 \cdot 1 0^{- 19})^{2}

\frac{1}{25 \cdot 2 ^{32} \cdot 5 ^{38}}

Decimal Notation

2.56 E - 38

Solution steps

(1.6 \cdot 1 0^{- 19})^{2}

Apply exponent rule:

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

(1.6 \cdot 1 0^{- 19})^{2} = 1. 6^{2} (1 0^{- 19})^{2}

= 1. 6^{2} (1 0^{- 19})^{2}

1. 6^{2} = 2.56

= 2.56 (1 0^{- 19})^{2}

Apply exponent rule:

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

(1 0^{- 19})^{2} = 1 0^{- 19 \cdot 2}

= 2.56 \cdot 1 0^{- 19 \cdot 2}

Multiply the numbers:

19 \cdot 2 = 38

= 2.56 \cdot 1 0^{- 38}

Apply exponent rule:

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

1 0^{- 38} = \frac{1}{1 0 ^{38}}

= 2.56 \cdot \frac{1}{1 0 ^{38}}

2.56 \cdot \frac{1}{1 0 ^{38}} = \frac{2.56}{1 0 ^{38}}

= \frac{2.56}{1 0 ^{38}}

\frac{2.56}{1 0 ^{38}} = \frac{256}{100 \cdot 1 0 ^{38}}

= \frac{256}{100 \cdot 1 0 ^{38}}

Factor the number:

256 = 4 \cdot 64

= \frac{4 \cdot 64}{100 \cdot 1 0 ^{38}}

Factor the number:

100 = 4 \cdot 25

= \frac{4 \cdot 64}{4 \cdot 25 \cdot 1 0 ^{38}}

Cancel the common factor:

4

= \frac{64}{25 \cdot 1 0 ^{38}}

Factor the number:

64 = 2^{6}

= \frac{2 ^{6}}{25 \cdot 1 0 ^{38}}

Factor

1 0^{38} : 2^{38} \cdot 5^{38}

= \frac{2 ^{6}}{25 \cdot 2 ^{38} \cdot 5 ^{38}}

\frac{2 ^{6}}{2 ^{38}} = \frac{1}{2 ^{32}}

= \frac{1}{25 \cdot 2 ^{32} \cdot 5 ^{38}}

500 - 80

(5 p^{2} q^{- 4})^{- 3}

y^{3} \cdot y^{4}

(3 a - 2 b^{2})^{3}

\frac{- 2.9 9 ^{3} + 27}{- 2.99 + 3}

What is (1.6*10^{-19})^2 ?
The solution to (1.6*10^{-19})^2 is 1/(25*2^{32)*5^{38}}