Solve (u^4v/2u^frac{1{2}v^-3})^9

$$( \frac { u ^ { 4 } v } { 2 u ^ { \frac { 1 } { 2 } } v ^ { - 3 } } ) ^ { 9 }$$

Evaluate

$$\frac{u^{\frac{63}{2}}v^{36}}{512}$$

Solution Steps

Cancel out \sqrt{u} in both numerator and denominator.

$$\left(\frac{vu^{\frac{7}{2}}}{2v^{-3}}\right)^{9}$$

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

$$\left(\frac{u^{\frac{7}{2}}v^{4}}{2}\right)^{9}$$

To raise \frac{u^{\frac{7}{2}}v^{4}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(u^{\frac{7}{2}}v^{4}\right)^{9}}{2^{9}}$$

Expand \left(u^{\frac{7}{2}}v^{4}\right)^{9}.

$$\frac{\left(u^{\frac{7}{2}}\right)^{9}\left(v^{4}\right)^{9}}{2^{9}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{2} and 9 to get \frac{63}{2}.

$$\frac{u^{\frac{63}{2}}\left(v^{4}\right)^{9}}{2^{9}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 9 to get 36.

$$\frac{u^{\frac{63}{2}}v^{36}}{2^{9}}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{u^{\frac{63}{2}}v^{36}}{512}$$

Expand

$$\frac{u^{\frac{63}{2}}v^{36}}{512}$$

Solution Steps

Cancel out \sqrt{u} in both numerator and denominator.

$$\left(\frac{vu^{\frac{7}{2}}}{2v^{-3}}\right)^{9}$$

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

$$\left(\frac{u^{\frac{7}{2}}v^{4}}{2}\right)^{9}$$

To raise \frac{u^{\frac{7}{2}}v^{4}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(u^{\frac{7}{2}}v^{4}\right)^{9}}{2^{9}}$$

Expand \left(u^{\frac{7}{2}}v^{4}\right)^{9}.

$$\frac{\left(u^{\frac{7}{2}}\right)^{9}\left(v^{4}\right)^{9}}{2^{9}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{2} and 9 to get \frac{63}{2}.

$$\frac{u^{\frac{63}{2}}\left(v^{4}\right)^{9}}{2^{9}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 9 to get 36.

$$\frac{u^{\frac{63}{2}}v^{36}}{2^{9}}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{u^{\frac{63}{2}}v^{36}}{512}$$