Solve (5/x^3)^2*(5/x)^-1

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

Evaluate

$$\frac{5}{x^{5}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{5^{1}}{x^{6}x^{-1}}$$

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

$$\frac{5^{1}}{x^{5}}$$

Calculate 5 to the power of 1 and get 5.

$$\frac{5}{x^{5}}$$

Expand

$$\frac{5}{x^{5}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{5^{1}}{x^{6}x^{-1}}$$

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

$$\frac{5^{1}}{x^{5}}$$

Calculate 5 to the power of 1 and get 5.

$$\frac{5}{x^{5}}$$