Solve (5x^-4y^3z^-2)^-4

$$( 5 x ^ { - 4 } y ^ { 3 } z ^ { - 2 } ) ^ { - 4 }$$

Evaluate

$$\frac{z^{8}x^{16}}{625y^{12}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(5x^{-4}y^{3}z^{-2}\right)^{-4}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$5^{-4}\left(x^{-4}\right)^{-4}\left(y^{3}\right)^{-4}\left(z^{-2}\right)^{-4}$$

Raise 5 to the power -4.

$$\frac{1}{625}\left(x^{-4}\right)^{-4}\left(y^{3}\right)^{-4}\left(z^{-2}\right)^{-4}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{625}x^{-4\left(-4\right)}y^{3\left(-4\right)}z^{-2\left(-4\right)}$$

Multiply -4 times -4.

$$\frac{1}{625}x^{16}y^{3\left(-4\right)}z^{-2\left(-4\right)}$$

Multiply 3 times -4.

$$\frac{1}{625}x^{16}\times \frac{1}{y^{12}}z^{-2\left(-4\right)}$$

Multiply -2 times -4.

$$\frac{1}{625}x^{16}\times \frac{1}{y^{12}}z^{8}$$

Expand

$$\frac{z^{8}x^{16}}{625y^{12}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(5x^{-4}y^{3}z^{-2}\right)^{-4}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$5^{-4}\left(x^{-4}\right)^{-4}\left(y^{3}\right)^{-4}\left(z^{-2}\right)^{-4}$$

Raise 5 to the power -4.

$$\frac{1}{625}\left(x^{-4}\right)^{-4}\left(y^{3}\right)^{-4}\left(z^{-2}\right)^{-4}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{625}x^{-4\left(-4\right)}y^{3\left(-4\right)}z^{-2\left(-4\right)}$$

Multiply -4 times -4.

$$\frac{1}{625}x^{16}y^{3\left(-4\right)}z^{-2\left(-4\right)}$$

Multiply 3 times -4.

$$\frac{1}{625}x^{16}\times \frac{1}{y^{12}}z^{-2\left(-4\right)}$$

Multiply -2 times -4.

$$\frac{1}{625}x^{16}\times \frac{1}{y^{12}}z^{8}$$