Solve -2^2-2^3left(-2^-1right)^21/{left(-{2^frac{1{2}}right)}^4}

$$\frac{ { -2 }^{ 2 } { -2 }^{ 3 } { \left(- { 2 }^{ -1 } \right) }^{ 21 } }{ { \left(- { 2 }^{ \frac{ 1 }{ 2 } } \right) }^{ 4 } }$$

Evaluate

$$\frac{1}{262144}=0.000003815$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\left(-2\right)^{5}\left(-2^{-1}\right)^{21}}{\left(-2^{\frac{1}{2}}\right)^{4}}$$

Calculate -2 to the power of 5 and get -32.

$$\frac{-32\left(-2^{-1}\right)^{21}}{\left(-2^{\frac{1}{2}}\right)^{4}}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$\frac{-32\left(-\frac{1}{2}\right)^{21}}{\left(-2^{\frac{1}{2}}\right)^{4}}$$

Calculate -\frac{1}{2} to the power of 21 and get -\frac{1}{2097152}.

$$\frac{-32\left(-\frac{1}{2097152}\right)}{\left(-2^{\frac{1}{2}}\right)^{4}}$$

Multiply -32 and -\frac{1}{2097152} to get \frac{1}{65536}.

$$\frac{\frac{1}{65536}}{\left(-2^{\frac{1}{2}}\right)^{4}}$$

Express \frac{\frac{1}{65536}}{\left(-2^{\frac{1}{2}}\right)^{4}} as a single fraction.

$$\frac{1}{65536\left(-2^{\frac{1}{2}}\right)^{4}}$$

Expand \left(-2^{\frac{1}{2}}\right)^{4}.

$$\frac{1}{65536\left(-1\right)^{4}\times \left(2^{\frac{1}{2}}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 4 to get 2.

$$\frac{1}{65536\left(-1\right)^{4}\times 2^{2}}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{1}{65536\times 1\times 2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{65536\times 1\times 4}$$

Multiply 1 and 4 to get 4.

$$\frac{1}{65536\times 4}$$

Multiply 65536 and 4 to get 262144.

$$\frac{1}{262144}$$

Factor

$$\frac{1}{2 ^ {18}} = 3.814697265625 \times 10^{-6}$$