Solve (2x^5/3x^-3)^2

$$( \frac { 2 x ^ { 5 } } { 3 x ^ { - 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{4x^{16}}{9}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{2x^{8}}{3}\right)^{2}$$

To raise \frac{2x^{8}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{8}\right)^{2}}{3^{2}}$$

Expand \left(2x^{8}\right)^{2}.

$$\frac{2^{2}\left(x^{8}\right)^{2}}{3^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{2^{2}x^{16}}{3^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{16}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4x^{16}}{9}$$

Expand

$$\frac{4x^{16}}{9}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{2x^{8}}{3}\right)^{2}$$

To raise \frac{2x^{8}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{8}\right)^{2}}{3^{2}}$$

Expand \left(2x^{8}\right)^{2}.

$$\frac{2^{2}\left(x^{8}\right)^{2}}{3^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{2^{2}x^{16}}{3^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{16}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4x^{16}}{9}$$