Simplify (4^-6)/((4^-3)^2)

$\frac{4^{- 6}}{{(4^{- 3})}^{2}}$

Step 1

Move $4^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(4^{- 3})}^{2} \cdot 4^{6}}$

Step 2

Simplify the denominator.

Multiply the exponents in ${(4^{- 3})}^{2}$ .

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

$\frac{1}{4^{- 3 \cdot 2} \cdot 4^{6}}$

Multiply $- 3$ by $2$ .

$\frac{1}{4^{- 6} \cdot 4^{6}}$

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

$\frac{1}{\frac{1}{4^{6}} \cdot 4^{6}}$

Raise $4$ to the power of $6$ .

$\frac{1}{\frac{1}{4096} \cdot 4^{6}}$

Raise $4$ to the power of $6$ .

$\frac{1}{\frac{1}{4096} \cdot 4096}$

Step 3

Combine fractions.

Combine $\frac{1}{4096}$ and $4096$ .

$\frac{1}{\frac{4096}{4096}}$

Simplify by dividing numbers.

Divide $4096$ by $4096$ .

$\frac{1}{1}$

Divide $1$ by $1$ .

$1$