Simplify (4^(-11/3))÷(4^(-2/3))

$4^{- \frac{11}{3}} \div 4^{- \frac{2}{3}}$

Step 1

Rewrite the division as a fraction.

$\frac{4^{- \frac{11}{3}}}{4^{- \frac{2}{3}}}$

Step 2

Move $4^{- \frac{11}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{4^{- \frac{2}{3}} \cdot 4^{\frac{11}{3}}}$

Step 3

Multiply $4^{- \frac{2}{3}}$ by $4^{\frac{11}{3}}$ by adding the exponents.

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

$\frac{1}{4^{- \frac{2}{3} + \frac{11}{3}}}$

Combine the numerators over the common denominator.

$\frac{1}{4^{\frac{- 2 + 11}{3}}}$

Add $- 2$ and $11$ .

$\frac{1}{4^{\frac{9}{3}}}$

Divide $9$ by $3$ .

$\frac{1}{4^{3}}$

Step 4

Raise $4$ to the power of $3$ .

$\frac{1}{64}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{64}$

Decimal Form:

$0.015625$