Solve (frac{5bsqrt{b}}{4})^2

$$( \frac { 5 b \sqrt { b } } { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{25b^{3}}{16}$$

Solution Steps

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

$$\frac{\left(5b\sqrt{b}\right)^{2}}{4^{2}}$$

Expand \left(5b\sqrt{b}\right)^{2}.

$$\frac{5^{2}b^{2}\left(\sqrt{b}\right)^{2}}{4^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25b^{2}\left(\sqrt{b}\right)^{2}}{4^{2}}$$

Calculate \sqrt{b} to the power of 2 and get b.

$$\frac{25b^{2}b}{4^{2}}$$

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

$$\frac{25b^{3}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{25b^{3}}{16}$$

Expand

$$\frac{25b^{3}}{16}$$

Solution Steps

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

$$\frac{\left(5b\sqrt{b}\right)^{2}}{4^{2}}$$

Expand \left(5b\sqrt{b}\right)^{2}.

$$\frac{5^{2}b^{2}\left(\sqrt{b}\right)^{2}}{4^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25b^{2}\left(\sqrt{b}\right)^{2}}{4^{2}}$$

Calculate \sqrt{b} to the power of 2 and get b.

$$\frac{25b^{2}b}{4^{2}}$$

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

$$\frac{25b^{3}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{25b^{3}}{16}$$