Solve (5x^7y^6z^5)^2

$$( 5 x ^ { 7 } y ^ { 6 } z ^ { 5 } ) ^ { 2 }$$

Evaluate

$$25z^{10}y^{12}x^{14}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(5x^{7}y^{6}z^{5}\right)^{2}$$

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

$$5^{2}\left(x^{7}\right)^{2}\left(y^{6}\right)^{2}\left(z^{5}\right)^{2}$$

Raise 5 to the power 2.

$$25\left(x^{7}\right)^{2}\left(y^{6}\right)^{2}\left(z^{5}\right)^{2}$$

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

$$25x^{7\times 2}y^{6\times 2}z^{5\times 2}$$

Multiply 7 times 2.

$$25x^{14}y^{6\times 2}z^{5\times 2}$$

Multiply 6 times 2.

$$25x^{14}y^{12}z^{5\times 2}$$

Multiply 5 times 2.

$$25x^{14}y^{12}z^{10}$$

Expand

$$25z^{10}y^{12}x^{14}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(5x^{7}y^{6}z^{5}\right)^{2}$$

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

$$5^{2}\left(x^{7}\right)^{2}\left(y^{6}\right)^{2}\left(z^{5}\right)^{2}$$

Raise 5 to the power 2.

$$25\left(x^{7}\right)^{2}\left(y^{6}\right)^{2}\left(z^{5}\right)^{2}$$

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

$$25x^{7\times 2}y^{6\times 2}z^{5\times 2}$$

Multiply 7 times 2.

$$25x^{14}y^{6\times 2}z^{5\times 2}$$

Multiply 6 times 2.

$$25x^{14}y^{12}z^{5\times 2}$$

Multiply 5 times 2.

$$25x^{14}y^{12}z^{10}$$