Solve (a^4/5a^-2/5)^-3

$$( \frac { a ^ { 4 } } { 5 a ^ { - 2 / 5 } } ) ^ { - 3 }$$

Evaluate

$$\frac{125}{a^{\frac{66}{5}}}$$

Solution Steps

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

$$\left(\frac{a^{\frac{22}{5}}}{5}\right)^{-3}$$

To raise \frac{a^{\frac{22}{5}}}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{\frac{22}{5}}\right)^{-3}}{5^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{22}{5} and -3 to get -\frac{66}{5}.

$$\frac{a^{-\frac{66}{5}}}{5^{-3}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{a^{-\frac{66}{5}}}{\frac{1}{125}}$$

Divide a^{-\frac{66}{5}} by \frac{1}{125} by multiplying a^{-\frac{66}{5}} by the reciprocal of \frac{1}{125}.

$$a^{-\frac{66}{5}}\times 125$$

Expand

$$\frac{125}{a^{\frac{66}{5}}}$$

Solution Steps

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

$$\left(\frac{a^{\frac{22}{5}}}{5}\right)^{-3}$$

To raise \frac{a^{\frac{22}{5}}}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{\frac{22}{5}}\right)^{-3}}{5^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{22}{5} and -3 to get -\frac{66}{5}.

$$\frac{a^{-\frac{66}{5}}}{5^{-3}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{a^{-\frac{66}{5}}}{\frac{1}{125}}$$

Divide a^{-\frac{66}{5}} by \frac{1}{125} by multiplying a^{-\frac{66}{5}} by the reciprocal of \frac{1}{125}.

$$a^{-\frac{66}{5}}\times 125$$