Solve {[-(1/4m^2)^2]^-6}^3=

$$\{ [ - ( \frac { 1 } { 4 } m ^ { 2 } ) ^ { 2 } ] ^ { - 6 } \} ^ { 3 } =$$

Evaluate

$$\frac{4722366482869645213696}{m^{72}}$$

Solution Steps

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

$$\left(\left(-\left(\frac{1}{4}\right)^{2}\left(m^{2}\right)^{2}\right)^{-6}\right)^{3}$$

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

$$\left(\left(-\left(\frac{1}{4}\right)^{2}m^{4}\right)^{-6}\right)^{3}$$

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

$$\left(\left(-\frac{1}{16}m^{4}\right)^{-6}\right)^{3}$$

Expand \left(-\frac{1}{16}m^{4}\right)^{-6}.

$$\left(\left(-\frac{1}{16}\right)^{-6}\left(m^{4}\right)^{-6}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -6 to get -24.

$$\left(\left(-\frac{1}{16}\right)^{-6}m^{-24}\right)^{3}$$

Calculate -\frac{1}{16} to the power of -6 and get 16777216.

$$\left(16777216m^{-24}\right)^{3}$$

Expand \left(16777216m^{-24}\right)^{3}.

$$16777216^{3}\left(m^{-24}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -24 and 3 to get -72.

$$16777216^{3}m^{-72}$$

Calculate 16777216 to the power of 3 and get 4722366482869645213696.

$$4722366482869645213696m^{-72}$$

Expand

$$\frac{4722366482869645213696}{m^{72}}$$

Solution Steps

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

$$\left(\left(-\left(\frac{1}{4}\right)^{2}\left(m^{2}\right)^{2}\right)^{-6}\right)^{3}$$

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

$$\left(\left(-\left(\frac{1}{4}\right)^{2}m^{4}\right)^{-6}\right)^{3}$$

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

$$\left(\left(-\frac{1}{16}m^{4}\right)^{-6}\right)^{3}$$

Expand \left(-\frac{1}{16}m^{4}\right)^{-6}.

$$\left(\left(-\frac{1}{16}\right)^{-6}\left(m^{4}\right)^{-6}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -6 to get -24.

$$\left(\left(-\frac{1}{16}\right)^{-6}m^{-24}\right)^{3}$$

Calculate -\frac{1}{16} to the power of -6 and get 16777216.

$$\left(16777216m^{-24}\right)^{3}$$

Expand \left(16777216m^{-24}\right)^{3}.

$$16777216^{3}\left(m^{-24}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -24 and 3 to get -72.

$$16777216^{3}m^{-72}$$

Calculate 16777216 to the power of 3 and get 4722366482869645213696.

$$4722366482869645213696m^{-72}$$