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

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

Evaluate

$$\frac{25c^{6}a^{7}}{2}$$

Solution Steps

Expand \left(5a^{3}c^{4}\right)^{2}.

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

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

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

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

$$\frac{5^{2}a^{6}c^{8}}{2a^{-1}c^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25a^{6}c^{8}}{2a^{-1}c^{2}}$$

Cancel out c^{2} in both numerator and denominator.

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

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

$$\frac{25c^{6}a^{7}}{2}$$

Expand

$$\frac{25c^{6}a^{7}}{2}$$

Solution Steps

Expand \left(5a^{3}c^{4}\right)^{2}.

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

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

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

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

$$\frac{5^{2}a^{6}c^{8}}{2a^{-1}c^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25a^{6}c^{8}}{2a^{-1}c^{2}}$$

Cancel out c^{2} in both numerator and denominator.

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

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

$$\frac{25c^{6}a^{7}}{2}$$