Solve 0.1^-4(-0.1)^2/0.1^4

$$\frac { 0.1 ^ { - 4 } ( - 0.1 ) ^ { 2 } } { 0.1 ^ { 4 } }$$

Evaluate

$$1000000$$

Solution Steps

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

$$\frac{\left(-0.1\right)^{2}}{0.1^{8}}$$

Calculate -0.1 to the power of 2 and get 0.01.

$$\frac{0.01}{0.1^{8}}$$

Calculate 0.1 to the power of 8 and get 0.00000001.

$$\frac{0.01}{0.00000001}$$

Expand \frac{0.01}{0.00000001} by multiplying both numerator and the denominator by 100000000. Anything divided by one gives itself.

$$1000000$$

Factor

$$2^{6}\times 5^{6}$$