Algebra Examples

$(4 \cdot 10^{- 1}) \cdot (2.5 \cdot 10^{- 4})$

Step 1

Multiply $4$ by $2.5$ .

$10 (10^{- 1} \cdot 10^{- 4})$

Step 2

Multiply $10^{- 1}$ by $10^{- 4}$ by adding the exponents.

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Step 2.1

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

$10 \cdot 10^{- 1 - 4}$

Step 2.2

Subtract $4$ from $- 1$ .

$10 \cdot 10^{- 5}$

Step 3

Move the decimal point in $10$ to the left by $1$ place and increase the power of $10^{- 5}$ by $1$ .

$1 \cdot 10^{- 4}$

Step 4

Multiply $10^{- 4}$ by $1$ .

$10^{- 4}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{10^{4}}$

Step 6

Raise $10$ to the power of $4$ .

$\frac{1}{10000}$