Solve frac{(4^{-3}x^{-2}y^{4})^-3}{-2^-6x^4y^-3}

$$\frac { ( 4 ^ { - 3 } x ^ { - 2 } y ^ { 4 } ) ^ { - 3 } } { - 2 ^ { - 6 } x ^ { 4 } y ^ { - 3 } }$$

Evaluate

$$-\frac{16777216x^{2}}{y^{9}}$$

Solution Steps

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

$$\frac{\left(\frac{1}{64}x^{-2}y^{4}\right)^{-3}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

Expand \left(\frac{1}{64}x^{-2}y^{4}\right)^{-3}.

$$\frac{\left(\frac{1}{64}\right)^{-3}\left(x^{-2}\right)^{-3}\left(y^{4}\right)^{-3}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

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

$$\frac{\left(\frac{1}{64}\right)^{-3}x^{6}\left(y^{4}\right)^{-3}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{\left(\frac{1}{64}\right)^{-3}x^{6}y^{-12}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

Calculate \frac{1}{64} to the power of -3 and get 262144.

$$\frac{262144x^{6}y^{-12}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

Calculate 2 to the power of -6 and get \frac{1}{64}.

$$\frac{262144x^{6}y^{-12}}{-\frac{1}{64}x^{4}y^{-3}}$$

Cancel out x^{4} in both numerator and denominator.

$$\frac{262144y^{-12}x^{2}}{-\frac{1}{64}y^{-3}}$$

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

$$\frac{262144x^{2}}{-\frac{1}{64}y^{9}}$$

Expand

$$-\frac{16777216x^{2}}{y^{9}}$$

Solution Steps

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

$$\frac{\left(\frac{1}{64}x^{-2}y^{4}\right)^{-3}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

Expand \left(\frac{1}{64}x^{-2}y^{4}\right)^{-3}.

$$\frac{\left(\frac{1}{64}\right)^{-3}\left(x^{-2}\right)^{-3}\left(y^{4}\right)^{-3}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

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

$$\frac{\left(\frac{1}{64}\right)^{-3}x^{6}\left(y^{4}\right)^{-3}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{\left(\frac{1}{64}\right)^{-3}x^{6}y^{-12}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

Calculate \frac{1}{64} to the power of -3 and get 262144.

$$\frac{262144x^{6}y^{-12}}{\left(-2^{-6}\right)x^{4}y^{-3}}$$

Calculate 2 to the power of -6 and get \frac{1}{64}.

$$\frac{262144x^{6}y^{-12}}{-\frac{1}{64}x^{4}y^{-3}}$$

Cancel out x^{4} in both numerator and denominator.

$$\frac{262144y^{-12}x^{2}}{-\frac{1}{64}y^{-3}}$$

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

$$\frac{262144x^{2}}{-\frac{1}{64}y^{9}}$$