Solve (x^-3/4x^-5)^-3

$$( \frac { x ^ { - 3 } } { 4 x ^ { - 5 } } ) ^ { - 3 }$$

Evaluate

$$\frac{64}{x^{6}}$$

Solution Steps

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

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

To raise \frac{x^{2}}{4} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{x^{-6}}{4^{-3}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{x^{-6}}{\frac{1}{64}}$$

Divide x^{-6} by \frac{1}{64} by multiplying x^{-6} by the reciprocal of \frac{1}{64}.

$$x^{-6}\times 64$$

Expand

$$\frac{64}{x^{6}}$$

Solution Steps

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

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

To raise \frac{x^{2}}{4} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{x^{-6}}{4^{-3}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{x^{-6}}{\frac{1}{64}}$$

Divide x^{-6} by \frac{1}{64} by multiplying x^{-6} by the reciprocal of \frac{1}{64}.

$$x^{-6}\times 64$$