Solve (2b^3)^4/(5b^7)^2

$$\frac { ( 2 b ^ { 3 } ) ^ { 4 } } { ( 5 b ^ { 7 } ) ^ { 2 } }$$

Evaluate

$$\frac{16}{25b^{2}}$$

Solution Steps

Expand \left(2b^{3}\right)^{4}.

$$\frac{2^{4}\left(b^{3}\right)^{4}}{\left(5b^{7}\right)^{2}}$$

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

$$\frac{2^{4}b^{12}}{\left(5b^{7}\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16b^{12}}{\left(5b^{7}\right)^{2}}$$

Expand \left(5b^{7}\right)^{2}.

$$\frac{16b^{12}}{5^{2}\left(b^{7}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{16b^{12}}{5^{2}b^{14}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{16b^{12}}{25b^{14}}$$

Cancel out b^{12} in both numerator and denominator.

$$\frac{16}{25b^{2}}$$

Expand

$$\frac{16}{25b^{2}}$$

Solution Steps

Expand \left(2b^{3}\right)^{4}.

$$\frac{2^{4}\left(b^{3}\right)^{4}}{\left(5b^{7}\right)^{2}}$$

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

$$\frac{2^{4}b^{12}}{\left(5b^{7}\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16b^{12}}{\left(5b^{7}\right)^{2}}$$

Expand \left(5b^{7}\right)^{2}.

$$\frac{16b^{12}}{5^{2}\left(b^{7}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{16b^{12}}{5^{2}b^{14}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{16b^{12}}{25b^{14}}$$

Cancel out b^{12} in both numerator and denominator.

$$\frac{16}{25b^{2}}$$