Solve (frac{a^{2}b^{3}}{c})^3*(c/a^3)^2*(1/b)^-2

$$( \frac { a ^ { 2 } b ^ { 3 } } { c } ) ^ { 3 } \cdot ( \frac { c } { a ^ { 3 } } ) ^ { 2 } \cdot ( \frac { 1 } { b } ) ^ { - 2 }$$

Evaluate

$$\frac{b^{11}}{c}$$

Solution Steps

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

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

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

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

To raise \frac{1}{b} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(a^{2}b^{3}\right)^{3}}{c^{3}} times \frac{c^{2}}{\left(a^{3}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply \frac{\left(a^{2}b^{3}\right)^{3}}{c\left(a^{3}\right)^{2}} times \frac{1^{-2}}{b^{-2}} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{\left(a^{2}b^{3}\right)^{3}\times 1^{-2}}{ca^{6}b^{-2}}$$

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

$$\frac{\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}\times 1^{-2}}{ca^{6}b^{-2}}$$

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

$$\frac{a^{6}\left(b^{3}\right)^{3}\times 1^{-2}}{ca^{6}b^{-2}}$$

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

$$\frac{a^{6}b^{9}\times 1^{-2}}{ca^{6}b^{-2}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{a^{6}b^{9}\times 1}{ca^{6}b^{-2}}$$

Cancel out a^{6} in both numerator and denominator.

$$\frac{b^{9}}{b^{-2}c}$$

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

$$\frac{b^{11}}{c}$$

Expand

$$\frac{b^{11}}{c}$$

Solution Steps

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

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

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

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

To raise \frac{1}{b} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(a^{2}b^{3}\right)^{3}}{c^{3}} times \frac{c^{2}}{\left(a^{3}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply \frac{\left(a^{2}b^{3}\right)^{3}}{c\left(a^{3}\right)^{2}} times \frac{1^{-2}}{b^{-2}} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{\left(a^{2}b^{3}\right)^{3}\times 1^{-2}}{ca^{6}b^{-2}}$$

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

$$\frac{\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}\times 1^{-2}}{ca^{6}b^{-2}}$$

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

$$\frac{a^{6}\left(b^{3}\right)^{3}\times 1^{-2}}{ca^{6}b^{-2}}$$

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

$$\frac{a^{6}b^{9}\times 1^{-2}}{ca^{6}b^{-2}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{a^{6}b^{9}\times 1}{ca^{6}b^{-2}}$$

Cancel out a^{6} in both numerator and denominator.

$$\frac{b^{9}}{b^{-2}c}$$

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

$$\frac{b^{11}}{c}$$