Solve left(5^2right)^4/left(5xright)^3*left(6xright)^-4/{left(6xright)^-6}

$$\frac{ { \left( { 5 }^{ 2 } \right) }^{ 4 } }{ { \left(5x \right) }^{ 3 } } \times \frac{ { \left(6x \right) }^{ -4 } }{ { \left(6x \right) }^{ -6 } }$$

Evaluate

$$\frac{112500}{x}$$

Solution Steps

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

$$\frac{5^{8}}{\left(5x\right)^{3}}\times \frac{\left(6x\right)^{-4}}{\left(6x\right)^{-6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from -4 to get 2.

$$\frac{5^{8}}{\left(5x\right)^{3}}\times \left(6x\right)^{2}$$

Calculate 5 to the power of 8 and get 390625.

$$\frac{390625}{\left(5x\right)^{3}}\times \left(6x\right)^{2}$$

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

$$\frac{390625}{5^{3}x^{3}}\times \left(6x\right)^{2}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{390625}{125x^{3}}\times \left(6x\right)^{2}$$

Expand \left(6x\right)^{2}.

$$\frac{390625}{125x^{3}}\times 6^{2}x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{390625}{125x^{3}}\times 36x^{2}$$

Express \frac{390625}{125x^{3}}\times 36 as a single fraction.

$$\frac{390625\times 36}{125x^{3}}x^{2}$$

Cancel out 125 in both numerator and denominator.

$$\frac{36\times 3125}{x^{3}}x^{2}$$

Express \frac{36\times 3125}{x^{3}}x^{2} as a single fraction.

$$\frac{36\times 3125x^{2}}{x^{3}}$$

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

$$\frac{36\times 3125}{x}$$

Multiply 36 and 3125 to get 112500.

$$\frac{112500}{x}$$

Expand

$$\frac{112500}{x}$$

Solution Steps

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

$$\frac{5^{8}}{\left(5x\right)^{3}}\times \frac{\left(6x\right)^{-4}}{\left(6x\right)^{-6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from -4 to get 2.

$$\frac{5^{8}}{\left(5x\right)^{3}}\times \left(6x\right)^{2}$$

Calculate 5 to the power of 8 and get 390625.

$$\frac{390625}{\left(5x\right)^{3}}\times \left(6x\right)^{2}$$

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

$$\frac{390625}{5^{3}x^{3}}\times \left(6x\right)^{2}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{390625}{125x^{3}}\times \left(6x\right)^{2}$$

Expand \left(6x\right)^{2}.

$$\frac{390625}{125x^{3}}\times 6^{2}x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{390625}{125x^{3}}\times 36x^{2}$$

Express \frac{390625}{125x^{3}}\times 36 as a single fraction.

$$\frac{390625\times 36}{125x^{3}}x^{2}$$

Cancel out 125 in both numerator and denominator.

$$\frac{36\times 3125}{x^{3}}x^{2}$$

Express \frac{36\times 3125}{x^{3}}x^{2} as a single fraction.

$$\frac{36\times 3125x^{2}}{x^{3}}$$

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

$$\frac{36\times 3125}{x}$$

Multiply 36 and 3125 to get 112500.

$$\frac{112500}{x}$$