Solve frac{(4b^{4}c^-4)^3}{3^-1b^-3c}

$$\frac { ( 4 b ^ { 4 } c ^ { - 4 } ) ^ { 3 } } { 3 ^ { - 1 } b ^ { - 3 } c }$$

Evaluate

$$\frac{192b^{15}}{c^{13}}$$

Solution Steps

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

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

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

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

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

$$\frac{4^{3}b^{12}c^{-12}}{3^{-1}b^{-3}c}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64b^{12}c^{-12}}{3^{-1}b^{-3}c}$$

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

$$\frac{64b^{12}c^{-12}}{\frac{1}{3}b^{-3}c}$$

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

$$\frac{64c^{-12}b^{15}}{\frac{1}{3}c}$$

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

$$\frac{64b^{15}}{\frac{1}{3}c^{13}}$$

Expand

$$\frac{192b^{15}}{c^{13}}$$

Solution Steps

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

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

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

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

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

$$\frac{4^{3}b^{12}c^{-12}}{3^{-1}b^{-3}c}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64b^{12}c^{-12}}{3^{-1}b^{-3}c}$$

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

$$\frac{64b^{12}c^{-12}}{\frac{1}{3}b^{-3}c}$$

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

$$\frac{64c^{-12}b^{15}}{\frac{1}{3}c}$$

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

$$\frac{64b^{15}}{\frac{1}{3}c^{13}}$$