Simplify (2^73^-4)(2^-53^4)

$(2^{7} \cdot 3^{- 4}) (2^{- 5} \cdot 3^{4})$

Step 1

Multiply $2^{7}$ by $2^{- 5}$ by adding the exponents.

Move $2^{- 5}$ .

$2^{- 5} \cdot 2^{7} \cdot 3^{- 4} \cdot 3^{4}$

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

$2^{- 5 + 7} \cdot 3^{- 4} \cdot 3^{4}$

Add $- 5$ and $7$ .

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

Step 2

Multiply $3^{- 4}$ by $3^{4}$ by adding the exponents.

Move $3^{4}$ .

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

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

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

Subtract $4$ from $4$ .

$2^{2} \cdot 3^{0}$

Step 3

Simplify $2^{2} \cdot 3^{0}$ .

$2^{2}$

Step 4

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

$4$

Simplify (2^7*3^-4)(2^-5*3^4)