Solve frac{15j^{5}k^2*25j^2k^4}{(5jk)^3}

$$\frac { 15 j ^ { 5 } k ^ { 2 } \cdot 25 j ^ { 2 } k ^ { 4 } } { ( 5 j k ) ^ { 3 } }$$

Evaluate

$$3k^{3}j^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{15j^{7}k^{2}\times 25k^{4}}{\left(5jk\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{15j^{7}k^{6}\times 25}{\left(5jk\right)^{3}}$$

Multiply 15 and 25 to get 375.

$$\frac{375j^{7}k^{6}}{\left(5jk\right)^{3}}$$

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

$$\frac{375j^{7}k^{6}}{5^{3}j^{3}k^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{375j^{7}k^{6}}{125j^{3}k^{3}}$$

Cancel out 125j^{3}k^{3} in both numerator and denominator.

$$3k^{3}j^{4}$$

Expand

$$3k^{3}j^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{15j^{7}k^{2}\times 25k^{4}}{\left(5jk\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{15j^{7}k^{6}\times 25}{\left(5jk\right)^{3}}$$

Multiply 15 and 25 to get 375.

$$\frac{375j^{7}k^{6}}{\left(5jk\right)^{3}}$$

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

$$\frac{375j^{7}k^{6}}{5^{3}j^{3}k^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{375j^{7}k^{6}}{125j^{3}k^{3}}$$

Cancel out 125j^{3}k^{3} in both numerator and denominator.

$$3k^{3}j^{4}$$