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

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

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

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

${(4^{- 2 - 3})}^{3}$

Subtract $3$ from $- 2$ .

${(4^{- 5})}^{3}$

Multiply the exponents in ${(4^{- 5})}^{3}$ .

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

$4^{- 5 \cdot 3}$

Multiply $- 5$ by $3$ .

$4^{- 15}$

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

$\frac{1}{4^{15}}$

Raise $4$ to the power of $15$ .

$\frac{1}{1073741824}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{1073741824}$

Decimal Form:

$9.31322574 \cdot 10^{- 10}$