Solve (5/3a^3b)^5:(5/6a^2)^5

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

Evaluate

$$32\left(ab\right)^{5}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{\left(\frac{5}{3}\right)^{5}a^{15}b^{5}}{\left(\frac{5}{6}a^{2}\right)^{5}}$$

Calculate \frac{5}{3} to the power of 5 and get \frac{3125}{243}.

$$\frac{\frac{3125}{243}a^{15}b^{5}}{\left(\frac{5}{6}a^{2}\right)^{5}}$$

Expand \left(\frac{5}{6}a^{2}\right)^{5}.

$$\frac{\frac{3125}{243}a^{15}b^{5}}{\left(\frac{5}{6}\right)^{5}\left(a^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{\frac{3125}{243}a^{15}b^{5}}{\left(\frac{5}{6}\right)^{5}a^{10}}$$

Calculate \frac{5}{6} to the power of 5 and get \frac{3125}{7776}.

$$\frac{\frac{3125}{243}a^{15}b^{5}}{\frac{3125}{7776}a^{10}}$$

Cancel out a^{10} in both numerator and denominator.

$$\frac{\frac{3125}{243}a^{5}b^{5}}{\frac{3125}{7776}}$$

Divide \frac{3125}{243}a^{5}b^{5} by \frac{3125}{7776} by multiplying \frac{3125}{243}a^{5}b^{5} by the reciprocal of \frac{3125}{7776}.

$$\frac{\frac{3125}{243}a^{5}b^{5}\times 7776}{3125}$$

Multiply \frac{3125}{243} and 7776 to get 100000.

$$\frac{100000a^{5}b^{5}}{3125}$$

Divide 100000a^{5}b^{5} by 3125 to get 32a^{5}b^{5}.

$$32a^{5}b^{5}$$

Expand

$$32\left(ab\right)^{5}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{\left(\frac{5}{3}\right)^{5}a^{15}b^{5}}{\left(\frac{5}{6}a^{2}\right)^{5}}$$

Calculate \frac{5}{3} to the power of 5 and get \frac{3125}{243}.

$$\frac{\frac{3125}{243}a^{15}b^{5}}{\left(\frac{5}{6}a^{2}\right)^{5}}$$

Expand \left(\frac{5}{6}a^{2}\right)^{5}.

$$\frac{\frac{3125}{243}a^{15}b^{5}}{\left(\frac{5}{6}\right)^{5}\left(a^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{\frac{3125}{243}a^{15}b^{5}}{\left(\frac{5}{6}\right)^{5}a^{10}}$$

Calculate \frac{5}{6} to the power of 5 and get \frac{3125}{7776}.

$$\frac{\frac{3125}{243}a^{15}b^{5}}{\frac{3125}{7776}a^{10}}$$

Cancel out a^{10} in both numerator and denominator.

$$\frac{\frac{3125}{243}a^{5}b^{5}}{\frac{3125}{7776}}$$

Divide \frac{3125}{243}a^{5}b^{5} by \frac{3125}{7776} by multiplying \frac{3125}{243}a^{5}b^{5} by the reciprocal of \frac{3125}{7776}.

$$\frac{\frac{3125}{243}a^{5}b^{5}\times 7776}{3125}$$

Multiply \frac{3125}{243} and 7776 to get 100000.

$$\frac{100000a^{5}b^{5}}{3125}$$

Divide 100000a^{5}b^{5} by 3125 to get 32a^{5}b^{5}.

$$32a^{5}b^{5}$$