Solve 4frac{(5a^{3}c^-1)^2}{(2a^-1c^2)}

$$4 \frac { ( 5 a ^ { 3 } c ^ { - 1 } ) ^ { 2 } } { ( 2 a ^ { - 1 } c ^ { 2 } ) }$$

Evaluate

$$\frac{50a^{7}}{c^{4}}$$

Solution Steps

Expand \left(5a^{3}c^{-1}\right)^{2}.

$$4\times \frac{5^{2}\left(a^{3}\right)^{2}\left(c^{-1}\right)^{2}}{2a^{-1}c^{2}}$$

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

$$4\times \frac{5^{2}a^{6}\left(c^{-1}\right)^{2}}{2a^{-1}c^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$4\times \frac{5^{2}a^{6}c^{-2}}{2a^{-1}c^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$4\times \frac{25a^{6}c^{-2}}{2a^{-1}c^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$4\times \frac{25c^{-2}a^{7}}{2c^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$4\times \frac{25a^{7}}{2c^{4}}$$

Express 4\times \frac{25a^{7}}{2c^{4}} as a single fraction.

$$\frac{4\times 25a^{7}}{2c^{4}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\times 25a^{7}}{c^{4}}$$

Multiply 2 and 25 to get 50.

$$\frac{50a^{7}}{c^{4}}$$

Expand

$$\frac{50a^{7}}{c^{4}}$$

Solution Steps

Expand \left(5a^{3}c^{-1}\right)^{2}.

$$4\times \frac{5^{2}\left(a^{3}\right)^{2}\left(c^{-1}\right)^{2}}{2a^{-1}c^{2}}$$

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

$$4\times \frac{5^{2}a^{6}\left(c^{-1}\right)^{2}}{2a^{-1}c^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$4\times \frac{5^{2}a^{6}c^{-2}}{2a^{-1}c^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$4\times \frac{25a^{6}c^{-2}}{2a^{-1}c^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$4\times \frac{25c^{-2}a^{7}}{2c^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$4\times \frac{25a^{7}}{2c^{4}}$$

Express 4\times \frac{25a^{7}}{2c^{4}} as a single fraction.

$$\frac{4\times 25a^{7}}{2c^{4}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\times 25a^{7}}{c^{4}}$$

Multiply 2 and 25 to get 50.

$$\frac{50a^{7}}{c^{4}}$$