Solve {left(1/6xy^3z^7right)}^2

$${ \left( \frac{ 1 }{ 6 } x { y }^{ 3 } { z }^{ 7 } \right) }^{ 2 }$$

Evaluate

$$\frac{x^{2}y^{6}z^{14}}{36}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{6}x^{1}y^{3}z^{7}\right)^{2}$$

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

$$\left(\frac{1}{6}\right)^{2}\left(x^{1}\right)^{2}\left(y^{3}\right)^{2}\left(z^{7}\right)^{2}$$

Raise \frac{1}{6} to the power 2.

$$\frac{1}{36}\left(x^{1}\right)^{2}\left(y^{3}\right)^{2}\left(z^{7}\right)^{2}$$

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

$$\frac{1}{36}x^{2}y^{3\times 2}z^{7\times 2}$$

Multiply 3 times 2.

$$\frac{1}{36}x^{2}y^{6}z^{7\times 2}$$

Multiply 7 times 2.

$$\frac{1}{36}x^{2}y^{6}z^{14}$$

Expand

$$\frac{x^{2}y^{6}z^{14}}{36}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{6}x^{1}y^{3}z^{7}\right)^{2}$$

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

$$\left(\frac{1}{6}\right)^{2}\left(x^{1}\right)^{2}\left(y^{3}\right)^{2}\left(z^{7}\right)^{2}$$

Raise \frac{1}{6} to the power 2.

$$\frac{1}{36}\left(x^{1}\right)^{2}\left(y^{3}\right)^{2}\left(z^{7}\right)^{2}$$

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

$$\frac{1}{36}x^{2}y^{3\times 2}z^{7\times 2}$$

Multiply 3 times 2.

$$\frac{1}{36}x^{2}y^{6}z^{7\times 2}$$

Multiply 7 times 2.

$$\frac{1}{36}x^{2}y^{6}z^{14}$$