Solve [frac{3a^{-2}b^{-3}c^{5}}{2a^-4b^-4c^1}]^3=

$$[ \frac { 3 a ^ { - 2 } b ^ { - 3 } c ^ { 5 } } { 2 a ^ { - 4 } b ^ { - 4 } c ^ { 1 } } ] ^ { 3 } =$$

Evaluate

$$\frac{27b^{3}a^{6}c^{12}}{8}$$

Solution Steps

Cancel out c in both numerator and denominator.

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

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

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

Calculate b to the power of 1 and get b.

$$\left(\frac{3ba^{2}c^{4}}{2}\right)^{3}$$

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

$$\frac{\left(3ba^{2}c^{4}\right)^{3}}{2^{3}}$$

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

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

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

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

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

$$\frac{3^{3}b^{3}a^{6}c^{12}}{2^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27b^{3}a^{6}c^{12}}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{27b^{3}a^{6}c^{12}}{8}$$

Expand

$$\frac{27b^{3}a^{6}c^{12}}{8}$$

Solution Steps

Cancel out c in both numerator and denominator.

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

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

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

Calculate b to the power of 1 and get b.

$$\left(\frac{3ba^{2}c^{4}}{2}\right)^{3}$$

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

$$\frac{\left(3ba^{2}c^{4}\right)^{3}}{2^{3}}$$

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

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

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

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

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

$$\frac{3^{3}b^{3}a^{6}c^{12}}{2^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27b^{3}a^{6}c^{12}}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{27b^{3}a^{6}c^{12}}{8}$$