Simplify 2^5*6^-5

$2^{5} \cdot 6^{- 5}$

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

$32 \cdot 6^{- 5}$

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

$32 \cdot \frac{1}{6^{5}}$

Raise $6$ to the power of $5$ .

$32 \cdot \frac{1}{7776}$

Cancel the common factor of $32$ .

Factor $32$ out of $7776$ .

$32 \cdot \frac{1}{32 (243)}$

Cancel the common factor.

$32 \cdot \frac{1}{32 \cdot 243}$

Rewrite the expression.

$\frac{1}{243}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{243}$

Decimal Form:

$0.00411522 \dots$