Solve (5xx^2/d^2)^2

$$( \frac { 5 x x ^ { 2 } } { d ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{25x^{6}}{d^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(\frac{5x^{3}}{d^{2}}\right)^{2}$$

To raise \frac{5x^{3}}{d^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5x^{3}\right)^{2}}{\left(d^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(5x^{3}\right)^{2}}{d^{4}}$$

Expand \left(5x^{3}\right)^{2}.

$$\frac{5^{2}\left(x^{3}\right)^{2}}{d^{4}}$$

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

$$\frac{5^{2}x^{6}}{d^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{6}}{d^{4}}$$

Expand

$$\frac{25x^{6}}{d^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(\frac{5x^{3}}{d^{2}}\right)^{2}$$

To raise \frac{5x^{3}}{d^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5x^{3}\right)^{2}}{\left(d^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(5x^{3}\right)^{2}}{d^{4}}$$

Expand \left(5x^{3}\right)^{2}.

$$\frac{5^{2}\left(x^{3}\right)^{2}}{d^{4}}$$

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

$$\frac{5^{2}x^{6}}{d^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{6}}{d^{4}}$$