Algebra Examples

$(2^{3} \cdot 5^{- 2}) (2^{- 2} \cdot 5^{4})$

Step 1

Multiply $2^{3}$ by $2^{- 2}$ by adding the exponents.

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Step 1.1

Move $2^{- 2}$ .

$2^{- 2} \cdot 2^{3} \cdot 5^{- 2} \cdot 5^{4}$

Step 1.2

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

$2^{- 2 + 3} \cdot 5^{- 2} \cdot 5^{4}$

Step 1.3

Add $- 2$ and $3$ .

$2^{1} \cdot 5^{- 2} \cdot 5^{4}$

Step 2

Simplify $2^{1} \cdot 5^{- 2} \cdot 5^{4}$ .

$2 \cdot 5^{- 2} \cdot 5^{4}$

Step 3

Multiply $5^{- 2}$ by $5^{4}$ by adding the exponents.

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Step 3.1

Move $5^{4}$ .

$2 \cdot (5^{4} \cdot 5^{- 2})$

Step 3.2

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

$2 \cdot 5^{4 - 2}$

Step 3.3

Subtract $2$ from $4$ .

$2 \cdot 5^{2}$

Step 4

Raise $5$ to the power of $2$ .

$2 \cdot 25$

Step 5

Multiply $2$ by $25$ .

$50$