Solve 4^{0}*4^3*4-(4^2)^3*4^frac{6{2}}

$$4 ^ { 0 } \cdot 4 ^ { 3 } \cdot 4 - ( 4 ^ { 2 } ) ^ { 3 } \cdot 4 ^ { \frac { 6 } { 2 } }$$

Evaluate

$$-261888$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 0 and 3 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$4^{4}-4^{6}\times 4^{\frac{6}{2}}$$

Calculate 4 to the power of 4 and get 256.

$$256-4^{6}\times 4^{\frac{6}{2}}$$

Calculate 4 to the power of 6 and get 4096.

$$256-4096\times 4^{\frac{6}{2}}$$

Divide 6 by 2 to get 3.

$$256-4096\times 4^{3}$$

Calculate 4 to the power of 3 and get 64.

$$256-4096\times 64$$

Multiply 4096 and 64 to get 262144.

$$256-262144$$

Subtract 262144 from 256 to get -261888.

$$-261888$$

Factor

$$-261888$$