Evaluate (6*6^-6)^5

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

Step 1

Multiply $6$ by $6^{- 6}$ by adding the exponents.

Multiply $6$ by $6^{- 6}$ .

Raise $6$ to the power of $1$ .

${(6^{1} \cdot 6^{- 6})}^{5}$

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

${(6^{1 - 6})}^{5}$

Subtract $6$ from $1$ .

${(6^{- 5})}^{5}$

Step 2

Multiply the exponents in ${(6^{- 5})}^{5}$ .

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

$6^{- 5 \cdot 5}$

Multiply $- 5$ by $5$ .

$6^{- 25}$

Step 3

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

$\frac{1}{6^{25}}$

Step 4

Raise $6$ to the power of $25$ .

$\frac{1}{28430288029929700000}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{28430288029929700000}$

Decimal Form:

$3.51737555 \cdot 10^{- 20}$