Solve [(4^{5}:4^{0}):4^4-2^3+(2^3)^0]

$$[ ( 4 ^ { 5 } : 4 ^ { 0 } ) : 4 ^ { 4 } - 2 ^ { 3 } + ( 2 ^ { 3 } ) ^ { 0 } ]$$

Evaluate

$$-3$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 0 from 5 to get 5.

$$\frac{4^{5}}{4^{4}}-2^{3}+\left(2^{3}\right)^{0}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$4^{1}-2^{3}+\left(2^{3}\right)^{0}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 0 to get 0.

$$4^{1}-2^{3}+2^{0}$$

Calculate 4 to the power of 1 and get 4.

$$4-2^{3}+2^{0}$$

Calculate 2 to the power of 3 and get 8.

$$4-8+2^{0}$$

Subtract 8 from 4 to get -4.

$$-4+2^{0}$$

Calculate 2 to the power of 0 and get 1.

$$-4+1$$

Add -4 and 1 to get -3.

$$-3$$

Factor

$$-3$$