What is (8*10^{-8})^2 ?

The solution to (8*10^{-8})^2 is 1/(5^{16)*1024}

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simplify (8*10^{-8})^2

simplify

(8 \cdot 1 0^{- 8})^{2}

\frac{1}{5 ^{16} \cdot 1024}

Decimal Notation

6.4 E - 15

Solution steps

(8 \cdot 1 0^{- 8})^{2}

Apply exponent rule:

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

(8 \cdot 1 0^{- 8})^{2} = 8^{2} (1 0^{- 8})^{2}

= 8^{2} (1 0^{- 8})^{2}

8^{2} = 64

= 64 (1 0^{- 8})^{2}

Apply exponent rule:

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

(1 0^{- 8})^{2} = 1 0^{- 8 \cdot 2}

= 64 \cdot 1 0^{- 8 \cdot 2}

Multiply the numbers:

8 \cdot 2 = 16

= 64 \cdot 1 0^{- 16}

Apply exponent rule:

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

1 0^{- 16} = \frac{1}{1 0 ^{16}}

= 64 \cdot \frac{1}{1 0 ^{16}}

Multiply fractions:

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

= \frac{1 \cdot 64}{1 0 ^{16}}

Multiply the numbers:

1 \cdot 64 = 64

= \frac{64}{1 0 ^{16}}

Factor

64 : 2^{6}

Factor

1 0^{16} : 2^{16} \cdot 5^{16}

= \frac{2 ^{6}}{2 ^{16} \cdot 5 ^{16}}

Cancel

\frac{2 ^{6}}{2 ^{16} \cdot 5 ^{16}} : \frac{1}{5 ^{16} \cdot 2 ^{10}}

= \frac{1}{5 ^{16} \cdot 2 ^{10}}

2^{10} = 1024

= \frac{1}{5 ^{16} \cdot 1024}

- \frac{1}{8} (\frac{4}{5} x - 24)

- 12 - 15

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