Solve (frac{2ab^{2}}{c^3})^2*(a^2c/b)^3=

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

Evaluate

$$\frac{4ba^{8}}{c^{3}}$$

Solution Steps

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

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

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

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

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

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

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

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

Expand \left(2ab^{2}\right)^{2}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

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

Cancel out b^{3}c^{3} in both numerator and denominator.

$$\frac{4ba^{8}}{c^{3}}$$

Expand

$$\frac{4ba^{8}}{c^{3}}$$

Solution Steps

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

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

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

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

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

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

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

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

Expand \left(2ab^{2}\right)^{2}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

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

Cancel out b^{3}c^{3} in both numerator and denominator.

$$\frac{4ba^{8}}{c^{3}}$$