Solve (frac{-4^{-2}m^4}{8m^-3p^2})^-2

$$( \frac { - 4 ^ { - 2 } m ^ { 4 } } { 8 m ^ { - 3 } p ^ { 2 } } ) ^ { - 2 }$$

Evaluate

$$\frac{16384p^{4}}{m^{14}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{\left(-4^{-2}\right)m^{7}}{8p^{2}}\right)^{-2}$$

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

$$\left(\frac{-\frac{1}{16}m^{7}}{8p^{2}}\right)^{-2}$$

To raise \frac{-\frac{1}{16}m^{7}}{8p^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-\frac{1}{16}m^{7}\right)^{-2}}{\left(8p^{2}\right)^{-2}}$$

Expand \left(-\frac{1}{16}m^{7}\right)^{-2}.

$$\frac{\left(-\frac{1}{16}\right)^{-2}\left(m^{7}\right)^{-2}}{\left(8p^{2}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{\left(-\frac{1}{16}\right)^{-2}m^{-14}}{\left(8p^{2}\right)^{-2}}$$

Calculate -\frac{1}{16} to the power of -2 and get 256.

$$\frac{256m^{-14}}{\left(8p^{2}\right)^{-2}}$$

Expand \left(8p^{2}\right)^{-2}.

$$\frac{256m^{-14}}{8^{-2}\left(p^{2}\right)^{-2}}$$

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

$$\frac{256m^{-14}}{8^{-2}p^{-4}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{256m^{-14}}{\frac{1}{64}p^{-4}}$$

Expand

$$\frac{16384p^{4}}{m^{14}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{\left(-4^{-2}\right)m^{7}}{8p^{2}}\right)^{-2}$$

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

$$\left(\frac{-\frac{1}{16}m^{7}}{8p^{2}}\right)^{-2}$$

To raise \frac{-\frac{1}{16}m^{7}}{8p^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-\frac{1}{16}m^{7}\right)^{-2}}{\left(8p^{2}\right)^{-2}}$$

Expand \left(-\frac{1}{16}m^{7}\right)^{-2}.

$$\frac{\left(-\frac{1}{16}\right)^{-2}\left(m^{7}\right)^{-2}}{\left(8p^{2}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{\left(-\frac{1}{16}\right)^{-2}m^{-14}}{\left(8p^{2}\right)^{-2}}$$

Calculate -\frac{1}{16} to the power of -2 and get 256.

$$\frac{256m^{-14}}{\left(8p^{2}\right)^{-2}}$$

Expand \left(8p^{2}\right)^{-2}.

$$\frac{256m^{-14}}{8^{-2}\left(p^{2}\right)^{-2}}$$

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

$$\frac{256m^{-14}}{8^{-2}p^{-4}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{256m^{-14}}{\frac{1}{64}p^{-4}}$$