Solve (2p^-3/p^5)^3

$$( \frac { 2 p ^ { - 3 } } { p ^ { 5 } } ) ^ { 3 }$$

Evaluate

$$\frac{8}{p^{24}}$$

Solution Steps

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

$$\left(\frac{2}{p^{8}}\right)^{3}$$

To raise \frac{2}{p^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2^{3}}{\left(p^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{2^{3}}{p^{24}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8}{p^{24}}$$

Expand

$$\frac{8}{p^{24}}$$

Solution Steps

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

$$\left(\frac{2}{p^{8}}\right)^{3}$$

To raise \frac{2}{p^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2^{3}}{\left(p^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{2^{3}}{p^{24}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8}{p^{24}}$$