Solve {[-(1/4m^2)^2]^-3}^3

$$\{ [ - ( \frac { 1 } { 4 } m ^ { 2 } ) ^ { 2 } ] ^ { - 3 } \} ^ { 3 }$$

Evaluate

$$-\frac{68719476736}{m^{36}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\left(-4096m^{-12}\right)^{3}$$

Expand \left(-4096m^{-12}\right)^{3}.

$$\left(-4096\right)^{3}\left(m^{-12}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -12 and 3 to get -36.

$$\left(-4096\right)^{3}m^{-36}$$

Calculate -4096 to the power of 3 and get -68719476736.

$$-68719476736m^{-36}$$

Expand

$$-\frac{68719476736}{m^{36}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\left(-4096m^{-12}\right)^{3}$$

Expand \left(-4096m^{-12}\right)^{3}.

$$\left(-4096\right)^{3}\left(m^{-12}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -12 and 3 to get -36.

$$\left(-4096\right)^{3}m^{-36}$$

Calculate -4096 to the power of 3 and get -68719476736.

$$-68719476736m^{-36}$$