Solve (4a^-4/a^2)^-2=

$$( \frac { 4 a ^ { - 4 } } { a ^ { 2 } } ) ^ { - 2 } =$$

Evaluate

$$\frac{a^{12}}{16}$$

Solution Steps

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

$$\left(\frac{4}{a^{6}}\right)^{-2}$$

To raise \frac{4}{a^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{4^{-2}}{\left(a^{6}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{4^{-2}}{a^{-12}}$$

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

$$\frac{\frac{1}{16}}{a^{-12}}$$

Express \frac{\frac{1}{16}}{a^{-12}} as a single fraction.

$$\frac{1}{16a^{-12}}$$

Expand

$$\frac{a^{12}}{16}$$

Solution Steps

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

$$\left(\frac{4}{a^{6}}\right)^{-2}$$

To raise \frac{4}{a^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{4^{-2}}{\left(a^{6}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{4^{-2}}{a^{-12}}$$

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

$$\frac{\frac{1}{16}}{a^{-12}}$$

Express \frac{\frac{1}{16}}{a^{-12}} as a single fraction.

$$\frac{1}{16a^{-12}}$$