Solve left(5a^3bright)^4left(a^2bright)^4/{left(5abright)^2}

$$\frac{ { \left(5 { a }^{ 3 } b \right) }^{ 4 } { \left( { a }^{ 2 } b \right) }^{ 4 } }{ { \left(5ab \right) }^{ 2 } }$$

Evaluate

$$25b^{6}a^{18}$$

Solution Steps

Expand \left(5a^{3}b\right)^{4}.

$$\frac{5^{4}\left(a^{3}\right)^{4}b^{4}\left(a^{2}b\right)^{4}}{\left(5ab\right)^{2}}$$

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

$$\frac{5^{4}a^{12}b^{4}\left(a^{2}b\right)^{4}}{\left(5ab\right)^{2}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{625a^{12}b^{4}\left(a^{2}b\right)^{4}}{\left(5ab\right)^{2}}$$

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

$$\frac{625a^{12}b^{4}\left(a^{2}\right)^{4}b^{4}}{\left(5ab\right)^{2}}$$

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

$$\frac{625a^{12}b^{4}a^{8}b^{4}}{\left(5ab\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 12 and 8 to get 20.

$$\frac{625a^{20}b^{4}b^{4}}{\left(5ab\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{625a^{20}b^{8}}{\left(5ab\right)^{2}}$$

Expand \left(5ab\right)^{2}.

$$\frac{625a^{20}b^{8}}{5^{2}a^{2}b^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{625a^{20}b^{8}}{25a^{2}b^{2}}$$

Cancel out 25a^{2}b^{2} in both numerator and denominator.

$$25b^{6}a^{18}$$

Expand

$$25b^{6}a^{18}$$

Solution Steps

Expand \left(5a^{3}b\right)^{4}.

$$\frac{5^{4}\left(a^{3}\right)^{4}b^{4}\left(a^{2}b\right)^{4}}{\left(5ab\right)^{2}}$$

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

$$\frac{5^{4}a^{12}b^{4}\left(a^{2}b\right)^{4}}{\left(5ab\right)^{2}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{625a^{12}b^{4}\left(a^{2}b\right)^{4}}{\left(5ab\right)^{2}}$$

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

$$\frac{625a^{12}b^{4}\left(a^{2}\right)^{4}b^{4}}{\left(5ab\right)^{2}}$$

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

$$\frac{625a^{12}b^{4}a^{8}b^{4}}{\left(5ab\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 12 and 8 to get 20.

$$\frac{625a^{20}b^{4}b^{4}}{\left(5ab\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{625a^{20}b^{8}}{\left(5ab\right)^{2}}$$

Expand \left(5ab\right)^{2}.

$$\frac{625a^{20}b^{8}}{5^{2}a^{2}b^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{625a^{20}b^{8}}{25a^{2}b^{2}}$$

Cancel out 25a^{2}b^{2} in both numerator and denominator.

$$25b^{6}a^{18}$$