Solve (frac{3x^{5}}{y^3})^2(3x^8/y)^-1

$$( \frac { 3 x ^ { 5 } } { y ^ { 3 } } ) ^ { 2 } ( \frac { 3 x ^ { 8 } } { y } ) ^ { - 1 }$$

Evaluate

$$\frac{3x^{2}}{y^{5}}$$

Solution Steps

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

$$\frac{\left(3x^{5}\right)^{2}}{\left(y^{3}\right)^{2}}\times \left(\frac{3x^{8}}{y}\right)^{-1}$$

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

$$\frac{\left(3x^{5}\right)^{2}}{\left(y^{3}\right)^{2}}\times \frac{\left(3x^{8}\right)^{-1}}{y^{-1}}$$

Multiply \frac{\left(3x^{5}\right)^{2}}{\left(y^{3}\right)^{2}} times \frac{\left(3x^{8}\right)^{-1}}{y^{-1}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x^{5}\right)^{2}\times \left(3x^{8}\right)^{-1}}{\left(y^{3}\right)^{2}y^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(3x^{5}\right)^{2}\times \left(3x^{8}\right)^{-1}}{y^{6}y^{-1}}$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$\frac{\left(3x^{5}\right)^{2}\times \left(3x^{8}\right)^{-1}}{y^{5}}$$

Expand \left(3x^{5}\right)^{2}.

$$\frac{3^{2}\left(x^{5}\right)^{2}\times \left(3x^{8}\right)^{-1}}{y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{3^{2}x^{10}\times \left(3x^{8}\right)^{-1}}{y^{5}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{10}\times \left(3x^{8}\right)^{-1}}{y^{5}}$$

Expand \left(3x^{8}\right)^{-1}.

$$\frac{9x^{10}\times 3^{-1}\left(x^{8}\right)^{-1}}{y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -1 to get -8.

$$\frac{9x^{10}\times 3^{-1}x^{-8}}{y^{5}}$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{9x^{10}\times \frac{1}{3}x^{-8}}{y^{5}}$$

Multiply 9 and \frac{1}{3} to get 3.

$$\frac{3x^{10}x^{-8}}{y^{5}}$$

To multiply powers of the same base, add their exponents. Add 10 and -8 to get 2.

$$\frac{3x^{2}}{y^{5}}$$

Expand

$$\frac{3x^{2}}{y^{5}}$$

Solution Steps

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

$$\frac{\left(3x^{5}\right)^{2}}{\left(y^{3}\right)^{2}}\times \left(\frac{3x^{8}}{y}\right)^{-1}$$

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

$$\frac{\left(3x^{5}\right)^{2}}{\left(y^{3}\right)^{2}}\times \frac{\left(3x^{8}\right)^{-1}}{y^{-1}}$$

Multiply \frac{\left(3x^{5}\right)^{2}}{\left(y^{3}\right)^{2}} times \frac{\left(3x^{8}\right)^{-1}}{y^{-1}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x^{5}\right)^{2}\times \left(3x^{8}\right)^{-1}}{\left(y^{3}\right)^{2}y^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(3x^{5}\right)^{2}\times \left(3x^{8}\right)^{-1}}{y^{6}y^{-1}}$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$\frac{\left(3x^{5}\right)^{2}\times \left(3x^{8}\right)^{-1}}{y^{5}}$$

Expand \left(3x^{5}\right)^{2}.

$$\frac{3^{2}\left(x^{5}\right)^{2}\times \left(3x^{8}\right)^{-1}}{y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{3^{2}x^{10}\times \left(3x^{8}\right)^{-1}}{y^{5}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{10}\times \left(3x^{8}\right)^{-1}}{y^{5}}$$

Expand \left(3x^{8}\right)^{-1}.

$$\frac{9x^{10}\times 3^{-1}\left(x^{8}\right)^{-1}}{y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -1 to get -8.

$$\frac{9x^{10}\times 3^{-1}x^{-8}}{y^{5}}$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{9x^{10}\times \frac{1}{3}x^{-8}}{y^{5}}$$

Multiply 9 and \frac{1}{3} to get 3.

$$\frac{3x^{10}x^{-8}}{y^{5}}$$

To multiply powers of the same base, add their exponents. Add 10 and -8 to get 2.

$$\frac{3x^{2}}{y^{5}}$$