What is (1*10^{-12})*10^{86/10} ?

The solution to (1*10^{-12})*10^{86/10} is 1/(1000*10^{2/5)}

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simplify (110^{-12})10^{86/10}

simplify

(1 \cdot 1 0^{- 12}) \cdot 1 0^{\frac{86}{10}}

\frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

Decimal Notation

0.00039 \dots

Solution steps

(1 \cdot 1 0^{- 12}) \cdot 1 0^{\frac{86}{10}}

Apply exponent rule:

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

= 1 \cdot 1 0^{\frac{86}{10}} \cdot \frac{1}{1 0 ^{12}}

1 0^{\frac{86}{10}} = 1 0^{8} \cdot 1 0^{\frac{3}{5}}

= 1 0^{8} \cdot 1 \cdot 1 0^{\frac{3}{5}} \cdot \frac{1}{1 0 ^{12}}

Factor integer

10 = 2 \cdot 5

= 1 \cdot \frac{1}{1 0 ^{12}} (2 \cdot 5)^{8} \cdot 1 0^{\frac{3}{5}}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 5)^{8} = 2^{8} \cdot 5^{8}

= 1 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{8} \cdot 5^{8} \cdot 1 0^{\frac{3}{5}}

Factor integer

10 = 2 \cdot 5

= 1 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{8} \cdot 5^{8} (2 \cdot 5)^{\frac{3}{5}}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

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

= 1 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{8} \cdot 5^{8} \cdot 2^{\frac{3}{5}} \cdot 5^{\frac{3}{5}}

Apply exponent rule:

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

5^{8} \cdot 5^{\frac{3}{5}} = 5^{8 + \frac{3}{5}}

= 1 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{8} \cdot 2^{\frac{3}{5}} \cdot 5^{8 + \frac{3}{5}}

5^{8 + \frac{3}{5}} = 5^{8} \cdot 5^{\frac{3}{5}}

= 2^{8} \cdot 5^{8} \cdot 1 \cdot 2^{\frac{3}{5}} \cdot 5^{\frac{3}{5}} \cdot \frac{1}{1 0 ^{12}}

Multiply fractions:

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

= 1 \cdot \frac{2 ^{8} \cdot 5 ^{8} \cdot 1 \cdot 2 ^{\frac{3}{5}} \cdot 5 ^{\frac{3}{5}}}{1 0 ^{12}}

\frac{1 \cdot 2 ^{8} \cdot 2 ^{\frac{3}{5}} \cdot 5 ^{8} \cdot 5 ^{\frac{3}{5}}}{1 0 ^{12}} = \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

= 1 \cdot \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

Multiply:

1 \cdot \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}} = \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

= \frac{1}{1000 \cdot 1 0 ^{\frac{2}{5}}}

\frac{( e ^{- 6.57611} )}{e ^{- 4.75235}}

(21 x + 2)^{\circ} (14 x + 3)^{\circ}

e^{(- 0)}

cos (2 t) e^{- t (s + 1)}

(\frac{4}{3})^{2 x - 3}

What is (1*10^{-12})*10^{86/10} ?
The solution to (1*10^{-12})*10^{86/10} is 1/(1000*10^{2/5)}