Simplify (6^2*6^5)^-6

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

Step 1

Multiply $6^{2}$ by $6^{5}$ by adding the exponents.

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

${(6^{2 + 5})}^{- 6}$

Add $2$ and $5$ .

${(6^{7})}^{- 6}$

Step 2

Multiply the exponents in ${(6^{7})}^{- 6}$ .

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

$6^{7 \cdot - 6}$

Multiply $7$ by $- 6$ .

$6^{- 42}$

Step 3

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

$\frac{1}{6^{42}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6^{42}}$

Decimal Form:

$2.07800928 \cdot 10^{- 33}$