Solve (4x^7y^4/8y^3)^4

$$( \frac { 4 x ^ { 7 } y ^ { 4 } } { 8 y ^ { 3 } } ) ^ { 4 }$$

Evaluate

$$\frac{y^{4}x^{28}}{16}$$

Solution Steps

Cancel out 4y^{3} in both numerator and denominator.

$$\left(\frac{yx^{7}}{2}\right)^{4}$$

To raise \frac{yx^{7}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(yx^{7}\right)^{4}}{2^{4}}$$

Expand \left(yx^{7}\right)^{4}.

$$\frac{y^{4}\left(x^{7}\right)^{4}}{2^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\frac{y^{4}x^{28}}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{y^{4}x^{28}}{16}$$

Expand

$$\frac{y^{4}x^{28}}{16}$$

Solution Steps

Cancel out 4y^{3} in both numerator and denominator.

$$\left(\frac{yx^{7}}{2}\right)^{4}$$

To raise \frac{yx^{7}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(yx^{7}\right)^{4}}{2^{4}}$$

Expand \left(yx^{7}\right)^{4}.

$$\frac{y^{4}\left(x^{7}\right)^{4}}{2^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\frac{y^{4}x^{28}}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{y^{4}x^{28}}{16}$$