Solve frac{(5x)^{-2}(x^{-3})^-4}{(25^-1x^-3)^-1}

$$\frac { ( 5 x ) ^ { - 2 } ( x ^ { - 3 } ) ^ { - 4 } } { ( 25 ^ { - 1 } x ^ { - 3 } ) ^ { - 1 } }$$

Evaluate

$$\frac{x^{7}}{625}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and -4 to get 12.

$$\frac{\left(5x\right)^{-2}x^{12}}{\left(25^{-1}x^{-3}\right)^{-1}}$$

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

$$\frac{5^{-2}x^{-2}x^{12}}{\left(25^{-1}x^{-3}\right)^{-1}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}x^{-2}x^{12}}{\left(25^{-1}x^{-3}\right)^{-1}}$$

To multiply powers of the same base, add their exponents. Add -2 and 12 to get 10.

$$\frac{\frac{1}{25}x^{10}}{\left(25^{-1}x^{-3}\right)^{-1}}$$

Calculate 25 to the power of -1 and get \frac{1}{25}.

$$\frac{\frac{1}{25}x^{10}}{\left(\frac{1}{25}x^{-3}\right)^{-1}}$$

Expand \left(\frac{1}{25}x^{-3}\right)^{-1}.

$$\frac{\frac{1}{25}x^{10}}{\left(\frac{1}{25}\right)^{-1}\left(x^{-3}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -1 to get 3.

$$\frac{\frac{1}{25}x^{10}}{\left(\frac{1}{25}\right)^{-1}x^{3}}$$

Calculate \frac{1}{25} to the power of -1 and get 25.

$$\frac{\frac{1}{25}x^{10}}{25x^{3}}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{\frac{1}{25}x^{7}}{25}$$

Divide \frac{1}{25}x^{7} by 25 to get \frac{1}{625}x^{7}.

$$\frac{1}{625}x^{7}$$

Expand

$$\frac{x^{7}}{625}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and -4 to get 12.

$$\frac{\left(5x\right)^{-2}x^{12}}{\left(25^{-1}x^{-3}\right)^{-1}}$$

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

$$\frac{5^{-2}x^{-2}x^{12}}{\left(25^{-1}x^{-3}\right)^{-1}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}x^{-2}x^{12}}{\left(25^{-1}x^{-3}\right)^{-1}}$$

To multiply powers of the same base, add their exponents. Add -2 and 12 to get 10.

$$\frac{\frac{1}{25}x^{10}}{\left(25^{-1}x^{-3}\right)^{-1}}$$

Calculate 25 to the power of -1 and get \frac{1}{25}.

$$\frac{\frac{1}{25}x^{10}}{\left(\frac{1}{25}x^{-3}\right)^{-1}}$$

Expand \left(\frac{1}{25}x^{-3}\right)^{-1}.

$$\frac{\frac{1}{25}x^{10}}{\left(\frac{1}{25}\right)^{-1}\left(x^{-3}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -1 to get 3.

$$\frac{\frac{1}{25}x^{10}}{\left(\frac{1}{25}\right)^{-1}x^{3}}$$

Calculate \frac{1}{25} to the power of -1 and get 25.

$$\frac{\frac{1}{25}x^{10}}{25x^{3}}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{\frac{1}{25}x^{7}}{25}$$

Divide \frac{1}{25}x^{7} by 25 to get \frac{1}{625}x^{7}.

$$\frac{1}{625}x^{7}$$