Solve (2b^2)^4/(5b^3)^6

$$\frac { ( 2 b ^ { 2 } ) ^ { 4 } } { ( 5 b ^ { 3 } ) ^ { 6 } }$$

Evaluate

$$\frac{16}{15625b^{10}}$$

Solution Steps

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

$$\frac{2^{4}\left(b^{2}\right)^{4}}{\left(5b^{3}\right)^{6}}$$

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

$$\frac{2^{4}b^{8}}{\left(5b^{3}\right)^{6}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16b^{8}}{\left(5b^{3}\right)^{6}}$$

Expand \left(5b^{3}\right)^{6}.

$$\frac{16b^{8}}{5^{6}\left(b^{3}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{16b^{8}}{5^{6}b^{18}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{16b^{8}}{15625b^{18}}$$

Cancel out b^{8} in both numerator and denominator.

$$\frac{16}{15625b^{10}}$$

Expand

$$\frac{16}{15625b^{10}}$$

Solution Steps

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

$$\frac{2^{4}\left(b^{2}\right)^{4}}{\left(5b^{3}\right)^{6}}$$

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

$$\frac{2^{4}b^{8}}{\left(5b^{3}\right)^{6}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16b^{8}}{\left(5b^{3}\right)^{6}}$$

Expand \left(5b^{3}\right)^{6}.

$$\frac{16b^{8}}{5^{6}\left(b^{3}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{16b^{8}}{5^{6}b^{18}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{16b^{8}}{15625b^{18}}$$

Cancel out b^{8} in both numerator and denominator.

$$\frac{16}{15625b^{10}}$$