Solve (2x)^-3/(5x)^-2

$$\frac { ( 2 x ) ^ { - 3 } } { ( 5 x ) ^ { - 2 } }$$

Evaluate

$$\frac{25}{8x}$$

Solution Steps

Expand \left(2x\right)^{-3}.

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

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}x^{-3}}{\left(5x\right)^{-2}}$$

Expand \left(5x\right)^{-2}.

$$\frac{\frac{1}{8}x^{-3}}{5^{-2}x^{-2}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{8}x^{-3}}{\frac{1}{25}x^{-2}}$$

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

$$\frac{\frac{1}{8}}{\frac{1}{25}x^{1}}$$

Calculate x to the power of 1 and get x.

$$\frac{\frac{1}{8}}{\frac{1}{25}x}$$

Express \frac{\frac{1}{8}}{\frac{1}{25}x} as a single fraction.

$$\frac{1}{8\times \frac{1}{25}x}$$

Multiply 8 and \frac{1}{25} to get \frac{8}{25}.

$$\frac{1}{\frac{8}{25}x}$$

Expand

$$\frac{25}{8x}$$

Solution Steps

Expand \left(2x\right)^{-3}.

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

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}x^{-3}}{\left(5x\right)^{-2}}$$

Expand \left(5x\right)^{-2}.

$$\frac{\frac{1}{8}x^{-3}}{5^{-2}x^{-2}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{8}x^{-3}}{\frac{1}{25}x^{-2}}$$

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

$$\frac{\frac{1}{8}}{\frac{1}{25}x^{1}}$$

Calculate x to the power of 1 and get x.

$$\frac{\frac{1}{8}}{\frac{1}{25}x}$$

Express \frac{\frac{1}{8}}{\frac{1}{25}x} as a single fraction.

$$\frac{1}{8\times \frac{1}{25}x}$$

Multiply 8 and \frac{1}{25} to get \frac{8}{25}.

$$\frac{1}{\frac{8}{25}x}$$