What is (5*10^{-10})^2 ?

The solution to (5*10^{-10})^2 is 1/(5^{18)*1048576}

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simplify (5*10^{-10})^2

simplify

(5 \cdot 1 0^{- 10})^{2}

\frac{1}{5 ^{18} \cdot 1048576}

Decimal Notation

2.5 E - 19

Solution steps

(5 \cdot 1 0^{- 10})^{2}

Apply exponent rule:

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

(5 \cdot 1 0^{- 10})^{2} = 5^{2} (1 0^{- 10})^{2}

= 5^{2} (1 0^{- 10})^{2}

5^{2} = 25

= 25 (1 0^{- 10})^{2}

Apply exponent rule:

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

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

= 25 \cdot 1 0^{- 10 \cdot 2}

Multiply the numbers:

10 \cdot 2 = 20

= 25 \cdot 1 0^{- 20}

Apply exponent rule:

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

1 0^{- 20} = \frac{1}{1 0 ^{20}}

= 25 \cdot \frac{1}{1 0 ^{20}}

Multiply fractions:

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

= \frac{1 \cdot 25}{1 0 ^{20}}

Multiply the numbers:

1 \cdot 25 = 25

= \frac{25}{1 0 ^{20}}

Factor

25 : 5^{2}

Factor

1 0^{20} : 2^{20} \cdot 5^{20}

= \frac{5 ^{2}}{2 ^{20} \cdot 5 ^{20}}

Cancel

\frac{5 ^{2}}{2 ^{20} \cdot 5 ^{20}} : \frac{1}{2 ^{20} \cdot 5 ^{18}}

= \frac{1}{2 ^{20} \cdot 5 ^{18}}

2^{20} = 1048576

= \frac{1}{5 ^{18} \cdot 1048576}

\frac{4 - 3 i}{3 + 2 i}

3 \frac{3}{10} \div 1 \frac{4}{7}

(- 32)^{2}

\frac{3 ( x - 2 )}{- ( 2 - x )}

(- \frac{27}{64})^{\frac{4}{3}}