Solve {[-(1/4m^2)^2]^8}^3=

$$\{ [ - ( \frac { 1 } { 4 } m ^ { 2 } ) ^ { 2 } ] ^ { 8 } \} ^ { 3 } =$$

Evaluate

$$\frac{m^{96}}{79228162514264337593543950336}$$

Solution Steps

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

$$\left(\left(-\left(\frac{1}{4}\right)^{2}\left(m^{2}\right)^{2}\right)^{8}\right)^{3}$$

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

$$\left(\left(-\left(\frac{1}{4}\right)^{2}m^{4}\right)^{8}\right)^{3}$$

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

$$\left(\left(-\frac{1}{16}m^{4}\right)^{8}\right)^{3}$$

Expand \left(-\frac{1}{16}m^{4}\right)^{8}.

$$\left(\left(-\frac{1}{16}\right)^{8}\left(m^{4}\right)^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 8 to get 32.

$$\left(\left(-\frac{1}{16}\right)^{8}m^{32}\right)^{3}$$

Calculate -\frac{1}{16} to the power of 8 and get \frac{1}{4294967296}.

$$\left(\frac{1}{4294967296}m^{32}\right)^{3}$$

Expand \left(\frac{1}{4294967296}m^{32}\right)^{3}.

$$\left(\frac{1}{4294967296}\right)^{3}\left(m^{32}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 32 and 3 to get 96.

$$\left(\frac{1}{4294967296}\right)^{3}m^{96}$$

Calculate \frac{1}{4294967296} to the power of 3 and get \frac{1}{79228162514264337593543950336}.

$$\frac{1}{79228162514264337593543950336}m^{96}$$

Expand

$$\frac{m^{96}}{79228162514264337593543950336}$$

Solution Steps

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

$$\left(\left(-\left(\frac{1}{4}\right)^{2}\left(m^{2}\right)^{2}\right)^{8}\right)^{3}$$

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

$$\left(\left(-\left(\frac{1}{4}\right)^{2}m^{4}\right)^{8}\right)^{3}$$

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

$$\left(\left(-\frac{1}{16}m^{4}\right)^{8}\right)^{3}$$

Expand \left(-\frac{1}{16}m^{4}\right)^{8}.

$$\left(\left(-\frac{1}{16}\right)^{8}\left(m^{4}\right)^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 8 to get 32.

$$\left(\left(-\frac{1}{16}\right)^{8}m^{32}\right)^{3}$$

Calculate -\frac{1}{16} to the power of 8 and get \frac{1}{4294967296}.

$$\left(\frac{1}{4294967296}m^{32}\right)^{3}$$

Expand \left(\frac{1}{4294967296}m^{32}\right)^{3}.

$$\left(\frac{1}{4294967296}\right)^{3}\left(m^{32}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 32 and 3 to get 96.

$$\left(\frac{1}{4294967296}\right)^{3}m^{96}$$

Calculate \frac{1}{4294967296} to the power of 3 and get \frac{1}{79228162514264337593543950336}.

$$\frac{1}{79228162514264337593543950336}m^{96}$$