Solve (4y^3/3y^-2)^3

$$( \frac { 4 y ^ { 3 } } { 3 y ^ { - 2 } } ) ^ { 3 }$$

Evaluate

$$\frac{64y^{15}}{27}$$

Solution Steps

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

$$\left(\frac{4y^{5}}{3}\right)^{3}$$

To raise \frac{4y^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4y^{5}\right)^{3}}{3^{3}}$$

Expand \left(4y^{5}\right)^{3}.

$$\frac{4^{3}\left(y^{5}\right)^{3}}{3^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{4^{3}y^{15}}{3^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64y^{15}}{3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{64y^{15}}{27}$$

Expand

$$\frac{64y^{15}}{27}$$

Solution Steps

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

$$\left(\frac{4y^{5}}{3}\right)^{3}$$

To raise \frac{4y^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4y^{5}\right)^{3}}{3^{3}}$$

Expand \left(4y^{5}\right)^{3}.

$$\frac{4^{3}\left(y^{5}\right)^{3}}{3^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{4^{3}y^{15}}{3^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64y^{15}}{3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{64y^{15}}{27}$$