Solve (frac{18a^{0}b^{5}c^3}{27b^2c^-1})^2

$$( \frac { 18 a ^ { 0 } b ^ { 5 } c ^ { 3 } } { 27 b ^ { 2 } c ^ { - 1 } } ) ^ { 2 }$$

Evaluate

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

Solution Steps

Cancel out 9b^{2} in both numerator and denominator.

$$\left(\frac{2a^{0}b^{3}c^{3}}{3\times \frac{1}{c}}\right)^{2}$$

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

$$\left(\frac{2a^{0}b^{3}c^{4}}{3}\right)^{2}$$

Calculate a to the power of 0 and get 1.

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

Multiply 2 and 1 to get 2.

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

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

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

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

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

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

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

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

$$\frac{2^{2}b^{6}c^{8}}{3^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4b^{6}c^{8}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

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

Expand

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

Solution Steps

Cancel out 9b^{2} in both numerator and denominator.

$$\left(\frac{2a^{0}b^{3}c^{3}}{3\times \frac{1}{c}}\right)^{2}$$

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

$$\left(\frac{2a^{0}b^{3}c^{4}}{3}\right)^{2}$$

Calculate a to the power of 0 and get 1.

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

Multiply 2 and 1 to get 2.

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

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

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

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

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

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

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

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

$$\frac{2^{2}b^{6}c^{8}}{3^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4b^{6}c^{8}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

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