Solve [(2*2^{3})]^-2div[(2^2*2*2^3)]^-2

$$[ ( 2 \cdot 2 ^ { 3 } ) ] ^ { - 2 } \div [ ( 2 ^ { 2 } \cdot 2 \cdot 2 ^ { 3 } ) ] ^ { - 2 }$$

Evaluate

$$16$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{2^{-8}}{\left(2^{6}\right)^{-2}}$$

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

$$\frac{2^{-8}}{2^{-12}}$$

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

$$2^{4}$$

Calculate 2 to the power of 4 and get 16.

$$16$$

Factor

$$2^{4}$$