Solve {left(a^3b^4c^3/4ab^2right)}^3

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

Evaluate

$$\frac{c^{9}\left(ab\right)^{6}}{64}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{a^{6}b^{6}c^{9}}{4^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{a^{6}b^{6}c^{9}}{64}$$

Expand

$$\frac{c^{9}\left(ab\right)^{6}}{64}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{a^{6}b^{6}c^{9}}{4^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{a^{6}b^{6}c^{9}}{64}$$