Solve (8^frac{4{3}})^5*4^-4div16^2=

$$( 8 ^ { \frac { 4 } { 3 } } ) ^ { 5 } \times 4 ^ { - 4 } \div 16 ^ { 2 } =$$

Evaluate

$$16$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{4}{3} and 5 to get \frac{20}{3}.

$$\frac{8^{\frac{20}{3}}\times 4^{-4}}{16^{2}}$$

Calculate 8 to the power of \frac{20}{3} and get 1048576.

$$\frac{1048576\times 4^{-4}}{16^{2}}$$

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{1048576\times \frac{1}{256}}{16^{2}}$$

Multiply 1048576 and \frac{1}{256} to get 4096.

$$\frac{4096}{16^{2}}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{4096}{256}$$

Divide 4096 by 256 to get 16.

$$16$$

Factor

$$2^{4}$$