Regroup using the commutative and associative properties.

[latex]\left(3\times6.8\right)\left(10^{8}\times10^{-13}\right)[/latex]

Multiply the coefficients.

[latex]\left(20.4\right)\left(10^{8}\times10^{-13}\right)[/latex]

Multiply the powers of [latex]10[/latex] using the Product Rule. Add the exponents.

[latex]20.4\times10^{-5}[/latex]

Convert [latex]20.4[/latex] into scientific notation by moving the decimal point one place to the left and multiplying by [latex]10^{1}[/latex].

[latex]\left(2.04\times10^{1}\right)\times10^{-5}[/latex]

Group the powers of [latex]10[/latex] using the associative property of multiplication.

[latex]2.04\times\left(10^{1}\times10^{-5}\right)[/latex]

Multiply using the Product Rule—add the exponents.

[latex]2.04\times10^{1+\left(-5\right)}[/latex]

Answer

[latex]\left(3\times10^{8}\right)\left(6.8\times10^{-13}\right)=2.04\times10^{-4}[/latex]

Regroup using the commutative and associative properties.

[latex]\left(8.2\times1.5\times1.9\right)\left(10^{6}\times10^{-3}\times10^{-7}\right)[/latex]

Multiply the numbers.

[latex]\left(23.37\right)\left(10^{6}\times10^{-3}\times10^{-7}\right)[/latex]

Multiply the powers of [latex]10[/latex] using the Product Rule—add the exponents.

[latex]23.37\times10^{-4}[/latex]

Convert [latex]23.37[/latex] into scientific notation by moving the decimal point one place to the left and multiplying by [latex]10^{1}[/latex].

[latex]\left(2.337\times10^{1}\right)\times10^{-4}[/latex]

Group the powers of [latex]10[/latex] using the associative property of multiplication.

[latex]2.337\times\left(10^{1}\times10^{-4}\right)[/latex]

Multiply using the Product Rule and add the exponents.

[latex]2.337\times10^{1+\left(-4\right)}[/latex]

Answer

[latex]\left(8.2\times10^{6}\right)\left(1.5\times10^{-3}\right)\left(1.9\times10^{-7}\right)=2.337\times10^{-3}[/latex]

Regroup using the associative property.

[latex] \displaystyle \left( \frac{2.829}{3.45} \right)\left( \frac{{{10}^{-9}}}{{{10}^{-3}}} \right)[/latex]

Divide the coefficients.

[latex] \displaystyle \left(0.82\right)\left( \frac{{{10}^{-9}}}{{{10}^{-3}}} \right)[/latex]

Divide the powers of [latex]10[/latex] using the Quotient Rule. Subtract the exponents.

[latex]\begin{array}{l}0.82\times10^{-9-\left(-3\right)}\\0.82\times10^{-6}\end{array}[/latex]

Convert [latex]0.82[/latex] into scientific notation by moving the decimal point one place to the right and multiplying by [latex]10^{-1}[/latex].

[latex]\left(8.2\times10^{-1}\right)\times10^{-6}[/latex]

Group the powers of [latex]10[/latex] together using the associative property.

[latex]8.2\times\left(10^{-1}\times10^{-6}\right)[/latex]

Multiply the powers of [latex]10[/latex] using the Product Rule—add the exponents.

[latex]8.2\times10^{-1+\left(-6\right)}[/latex]

Answer

[latex] \displaystyle \frac{2.829\times {{10}^{-9}}}{3.45\times {{10}^{-3}}}=8.2\times {{10}^{-7}}[/latex]

Regroup the terms in the numerator according to the associative and commutative properties.

[latex] \displaystyle \frac{\left( 1.37\times 9.85 \right)\left( {{10}^{6}}\times {{10}^{4}} \right)}{5.0\times {{10}^{12}}}[/latex]

Multiply.

[latex] \displaystyle \frac{13.4945\times {{10}^{10}}}{5.0\times {{10}^{12}}}[/latex]

Regroup using the associative property.

[latex] \displaystyle \left( \frac{13.4945}{5.0} \right)\left( \frac{{{10}^{10}}}{{{10}^{12}}} \right)[/latex]

Divide the numbers.

[latex] \displaystyle \left(2.6989\right)\left(\frac{10^{10}}{10^{12}}\right)[/latex]

Divide the powers of [latex]10[/latex] using the Quotient Rule—subtract the exponents.

[latex] \displaystyle \begin{array}{c}\left(2.6989 \right)\left( {{10}^{10-12}} \right)\\2.6989\times {{10}^{-2}}\end{array}[/latex]

Answer

[latex] \displaystyle \frac{\left( 1.37\times {{10}^{4}} \right)\left( 9.85\times {{10}^{6}} \right)}{5.0\times {{10}^{12}}}=2.6989\times {{10}^{-2}}[/latex]