Solve (5r^30s^-4)^2

$$( 5 r ^ { 30 } s ^ { - 4 } ) ^ { 2 }$$

Evaluate

$$\frac{25r^{60}}{s^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5r^{30}s^{-4}\right)^{2}$$

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

$$5^{2}\left(r^{30}\right)^{2}\left(s^{-4}\right)^{2}$$

Raise 5 to the power 2.

$$25\left(r^{30}\right)^{2}\left(s^{-4}\right)^{2}$$

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

$$25r^{30\times 2}s^{-4\times 2}$$

Multiply 30 times 2.

$$25r^{60}s^{-4\times 2}$$

Multiply -4 times 2.

$$25r^{60}\times \frac{1}{s^{8}}$$

Expand

$$\frac{25r^{60}}{s^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5r^{30}s^{-4}\right)^{2}$$

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

$$5^{2}\left(r^{30}\right)^{2}\left(s^{-4}\right)^{2}$$

Raise 5 to the power 2.

$$25\left(r^{30}\right)^{2}\left(s^{-4}\right)^{2}$$

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

$$25r^{30\times 2}s^{-4\times 2}$$

Multiply 30 times 2.

$$25r^{60}s^{-4\times 2}$$

Multiply -4 times 2.

$$25r^{60}\times \frac{1}{s^{8}}$$