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

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

Evaluate

$$\frac{64b^{6}c^{15}}{27a^{21}}$$

Solution Steps

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

$$\left(\frac{3b^{-6}c^{-3}a^{7}}{4b^{-4}c^{2}}\right)^{-3}$$

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

$$\left(\frac{3a^{7}}{4b^{2}c^{5}}\right)^{-3}$$

To raise \frac{3a^{7}}{4b^{2}c^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3a^{7}\right)^{-3}}{\left(4b^{2}c^{5}\right)^{-3}}$$

Expand \left(3a^{7}\right)^{-3}.

$$\frac{3^{-3}\left(a^{7}\right)^{-3}}{\left(4b^{2}c^{5}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -3 to get -21.

$$\frac{3^{-3}a^{-21}}{\left(4b^{2}c^{5}\right)^{-3}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{27}a^{-21}}{\left(4b^{2}c^{5}\right)^{-3}}$$

Expand \left(4b^{2}c^{5}\right)^{-3}.

$$\frac{\frac{1}{27}a^{-21}}{4^{-3}\left(b^{2}\right)^{-3}\left(c^{5}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}a^{-21}}{4^{-3}b^{-6}\left(c^{5}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{\frac{1}{27}a^{-21}}{4^{-3}b^{-6}c^{-15}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{\frac{1}{27}a^{-21}}{\frac{1}{64}b^{-6}c^{-15}}$$

Expand

$$\frac{64b^{6}c^{15}}{27a^{21}}$$

Solution Steps

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

$$\left(\frac{3b^{-6}c^{-3}a^{7}}{4b^{-4}c^{2}}\right)^{-3}$$

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

$$\left(\frac{3a^{7}}{4b^{2}c^{5}}\right)^{-3}$$

To raise \frac{3a^{7}}{4b^{2}c^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3a^{7}\right)^{-3}}{\left(4b^{2}c^{5}\right)^{-3}}$$

Expand \left(3a^{7}\right)^{-3}.

$$\frac{3^{-3}\left(a^{7}\right)^{-3}}{\left(4b^{2}c^{5}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -3 to get -21.

$$\frac{3^{-3}a^{-21}}{\left(4b^{2}c^{5}\right)^{-3}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{27}a^{-21}}{\left(4b^{2}c^{5}\right)^{-3}}$$

Expand \left(4b^{2}c^{5}\right)^{-3}.

$$\frac{\frac{1}{27}a^{-21}}{4^{-3}\left(b^{2}\right)^{-3}\left(c^{5}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}a^{-21}}{4^{-3}b^{-6}\left(c^{5}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{\frac{1}{27}a^{-21}}{4^{-3}b^{-6}c^{-15}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{\frac{1}{27}a^{-21}}{\frac{1}{64}b^{-6}c^{-15}}$$