Solve left(4^-3x^-2y^4right)^-3/{2^-6{x}^4{y}^-3}

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{262144x^{6}y^{-12}}{2^{-6}x^{4}y^{-3}}$$

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}.

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

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

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

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

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

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

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

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

$$\frac{262144x^{6}y^{-12}}{2^{-6}x^{4}y^{-3}}$$

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.

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