Solve (a^{-2}b^{6}c^{-2})^{-2}*(a^-1b^3c^-frac{5{4}})^4

$$( a ^ { - 2 } b ^ { 6 } c ^ { - 2 } ) ^ { - 2 } \cdot ( a ^ { - 1 } b ^ { 3 } c ^ { - \frac { 5 } { 4 } } ) ^ { 4 }$$

Evaluate

$$\frac{1}{c}$$

Solution Steps

Expand \left(a^{-2}b^{6}c^{-2}\right)^{-2}.

$$\left(a^{-2}\right)^{-2}\left(b^{6}\right)^{-2}\left(c^{-2}\right)^{-2}\left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}$$

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

$$a^{4}\left(b^{6}\right)^{-2}\left(c^{-2}\right)^{-2}\left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}$$

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

$$a^{4}b^{-12}\left(c^{-2}\right)^{-2}\left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}$$

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

$$a^{4}b^{-12}c^{4}\left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}$$

Expand \left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}.

$$a^{4}b^{-12}c^{4}\left(a^{-1}\right)^{4}\left(b^{3}\right)^{4}\left(c^{-\frac{5}{4}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

$$a^{4}b^{-12}c^{4}a^{-4}\left(b^{3}\right)^{4}\left(c^{-\frac{5}{4}}\right)^{4}$$

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

$$a^{4}b^{-12}c^{4}a^{-4}b^{12}\left(c^{-\frac{5}{4}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{5}{4} and 4 to get -5.

$$a^{4}b^{-12}c^{4}a^{-4}b^{12}c^{-5}$$

Multiply a^{4} and a^{-4} to get 1.

$$b^{-12}c^{4}b^{12}c^{-5}$$

Multiply b^{-12} and b^{12} to get 1.

$$c^{4}c^{-5}$$

To multiply powers of the same base, add their exponents. Add 4 and -5 to get -1.

$$c^{-1}$$

Expand

$$\frac{1}{c}$$

Solution Steps

Expand \left(a^{-2}b^{6}c^{-2}\right)^{-2}.

$$\left(a^{-2}\right)^{-2}\left(b^{6}\right)^{-2}\left(c^{-2}\right)^{-2}\left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}$$

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

$$a^{4}\left(b^{6}\right)^{-2}\left(c^{-2}\right)^{-2}\left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}$$

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

$$a^{4}b^{-12}\left(c^{-2}\right)^{-2}\left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}$$

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

$$a^{4}b^{-12}c^{4}\left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}$$

Expand \left(a^{-1}b^{3}c^{-\frac{5}{4}}\right)^{4}.

$$a^{4}b^{-12}c^{4}\left(a^{-1}\right)^{4}\left(b^{3}\right)^{4}\left(c^{-\frac{5}{4}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

$$a^{4}b^{-12}c^{4}a^{-4}\left(b^{3}\right)^{4}\left(c^{-\frac{5}{4}}\right)^{4}$$

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

$$a^{4}b^{-12}c^{4}a^{-4}b^{12}\left(c^{-\frac{5}{4}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{5}{4} and 4 to get -5.

$$a^{4}b^{-12}c^{4}a^{-4}b^{12}c^{-5}$$

Multiply a^{4} and a^{-4} to get 1.

$$b^{-12}c^{4}b^{12}c^{-5}$$

Multiply b^{-12} and b^{12} to get 1.

$$c^{4}c^{-5}$$

To multiply powers of the same base, add their exponents. Add 4 and -5 to get -1.

$$c^{-1}$$