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Evaluate (0.410^4)(210^-13)

$(0.4 \cdot 10^{4}) (2 \cdot 10^{- 13})$

Step 1

Multiply $0.4$ by $2$ .

$0.8 (10^{4} \cdot 10^{- 13})$

Step 2

Multiply $10^{4}$ by $10^{- 13}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$0.8 \cdot 10^{4 - 13}$

Subtract $13$ from $4$ .

$0.8 \cdot 10^{- 9}$

$0.8 \cdot 10^{- 9}$

Step 3

Move the decimal point in $0.8$ to the right by $1$ place and decrease the power of $10^{- 9}$ by $1$ .

$8 \cdot 10^{- 10}$

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