Evaluate 6^5*(6^-2)^3

$6^{5} \cdot {(6^{- 2})}^{3}$

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

$7776 \cdot {(6^{- 2})}^{3}$

Multiply the exponents in ${(6^{- 2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$7776 \cdot 6^{- 2 \cdot 3}$

Multiply $- 2$ by $3$ .

$7776 \cdot 6^{- 6}$

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

$7776 \cdot \frac{1}{6^{6}}$

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

$7776 \cdot \frac{1}{46656}$

Cancel the common factor of $7776$ .

Factor $7776$ out of $46656$ .

$7776 \cdot \frac{1}{7776 (6)}$

Cancel the common factor.

$7776 \cdot \frac{1}{7776 \cdot 6}$

Rewrite the expression.

$\frac{1}{6}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$