Simplify (2^-33^-5)(2^43^3)

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

Multiply $2^{- 3}$ by $2^{4}$ by adding the exponents.

Move $2^{4}$ .

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

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

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

Subtract $3$ from $4$ .

$2^{1} \cdot 3^{- 5} \cdot 3^{3}$

Simplify $2^{1} \cdot 3^{- 5} \cdot 3^{3}$ .

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

Multiply $3^{- 5}$ by $3^{3}$ by adding the exponents.

Move $3^{3}$ .

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

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

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

Subtract $5$ from $3$ .

$2 \cdot 3^{- 2}$

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

$2 \cdot \frac{1}{3^{2}}$

Raise $3$ to the power of $2$ .

$2 \cdot \frac{1}{9}$

Combine $2$ and $\frac{1}{9}$ .

$\frac{2}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{9}$

Decimal Form:

$0.\overline{2}$

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