Solve (2b^{2}c^{-4})^3(3b^-4c^-2)^-2

$$( 2 b ^ { 2 } c ^ { - 4 } ) ^ { 3 } ( 3 b ^ { - 4 } c ^ { - 2 } ) ^ { - 2 }$$

Evaluate

$$\frac{8b^{14}}{9c^{8}}$$

Solution Steps

Expand \left(2b^{2}c^{-4}\right)^{3}.

$$2^{3}\left(b^{2}\right)^{3}\left(c^{-4}\right)^{3}\times \left(3b^{-4}c^{-2}\right)^{-2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$2^{3}b^{6}\left(c^{-4}\right)^{3}\times \left(3b^{-4}c^{-2}\right)^{-2}$$

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

$$2^{3}b^{6}c^{-12}\times \left(3b^{-4}c^{-2}\right)^{-2}$$

Calculate 2 to the power of 3 and get 8.

$$8b^{6}c^{-12}\times \left(3b^{-4}c^{-2}\right)^{-2}$$

Expand \left(3b^{-4}c^{-2}\right)^{-2}.

$$8b^{6}c^{-12}\times 3^{-2}\left(b^{-4}\right)^{-2}\left(c^{-2}\right)^{-2}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.

$$8b^{6}c^{-12}\times 3^{-2}b^{8}\left(c^{-2}\right)^{-2}$$

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

$$8b^{6}c^{-12}\times 3^{-2}b^{8}c^{4}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$8b^{6}c^{-12}\times \frac{1}{9}b^{8}c^{4}$$

Multiply 8 and \frac{1}{9} to get \frac{8}{9}.

$$\frac{8}{9}b^{6}c^{-12}b^{8}c^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$\frac{8}{9}b^{14}c^{-12}c^{4}$$

To multiply powers of the same base, add their exponents. Add -12 and 4 to get -8.

$$\frac{8}{9}b^{14}c^{-8}$$

Expand

$$\frac{8b^{14}}{9c^{8}}$$

Solution Steps

Expand \left(2b^{2}c^{-4}\right)^{3}.

$$2^{3}\left(b^{2}\right)^{3}\left(c^{-4}\right)^{3}\times \left(3b^{-4}c^{-2}\right)^{-2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$2^{3}b^{6}\left(c^{-4}\right)^{3}\times \left(3b^{-4}c^{-2}\right)^{-2}$$

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

$$2^{3}b^{6}c^{-12}\times \left(3b^{-4}c^{-2}\right)^{-2}$$

Calculate 2 to the power of 3 and get 8.

$$8b^{6}c^{-12}\times \left(3b^{-4}c^{-2}\right)^{-2}$$

Expand \left(3b^{-4}c^{-2}\right)^{-2}.

$$8b^{6}c^{-12}\times 3^{-2}\left(b^{-4}\right)^{-2}\left(c^{-2}\right)^{-2}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.

$$8b^{6}c^{-12}\times 3^{-2}b^{8}\left(c^{-2}\right)^{-2}$$

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

$$8b^{6}c^{-12}\times 3^{-2}b^{8}c^{4}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$8b^{6}c^{-12}\times \frac{1}{9}b^{8}c^{4}$$

Multiply 8 and \frac{1}{9} to get \frac{8}{9}.

$$\frac{8}{9}b^{6}c^{-12}b^{8}c^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$\frac{8}{9}b^{14}c^{-12}c^{4}$$

To multiply powers of the same base, add their exponents. Add -12 and 4 to get -8.

$$\frac{8}{9}b^{14}c^{-8}$$