Solve =((-4)^2)^6:(-4)^8:2^3

$$= ( ( - 4 ) ^ { 2 } ) ^ { 6 } : ( - 4 ) ^ { 8 } : 2 ^ { 3 }$$

Evaluate

$$32$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{\frac{\left(-4\right)^{12}}{\left(-4\right)^{8}}}{2^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 8 from 12 to get 4.

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

Calculate -4 to the power of 4 and get 256.

$$\frac{256}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{256}{8}$$

Divide 256 by 8 to get 32.

$$32$$

Factor

$$2^{5}$$