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

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

Evaluate

$$-\frac{m^{12}}{4096}$$

Solution Steps

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

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

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

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

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\left(\left(-\frac{1}{16}m^{4}\right)^{1}\right)^{3}$$

Calculate -\frac{1}{16}m^{4} to the power of 1 and get -\frac{1}{16}m^{4}.

$$\left(-\frac{1}{16}m^{4}\right)^{3}$$

Expand \left(-\frac{1}{16}m^{4}\right)^{3}.

$$\left(-\frac{1}{16}\right)^{3}\left(m^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-\frac{1}{16}\right)^{3}m^{12}$$

Calculate -\frac{1}{16} to the power of 3 and get -\frac{1}{4096}.

$$-\frac{1}{4096}m^{12}$$

Expand

$$-\frac{m^{12}}{4096}$$

Solution Steps

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

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

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

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

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\left(\left(-\frac{1}{16}m^{4}\right)^{1}\right)^{3}$$

Calculate -\frac{1}{16}m^{4} to the power of 1 and get -\frac{1}{16}m^{4}.

$$\left(-\frac{1}{16}m^{4}\right)^{3}$$

Expand \left(-\frac{1}{16}m^{4}\right)^{3}.

$$\left(-\frac{1}{16}\right)^{3}\left(m^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-\frac{1}{16}\right)^{3}m^{12}$$

Calculate -\frac{1}{16} to the power of 3 and get -\frac{1}{4096}.

$$-\frac{1}{4096}m^{12}$$