Solve [(0,4)^2]^10div[(0,4)^9*(0,4)^7*(0,4)]=

$$[ ( 0,4 ) ^ { 2 } ] ^ { 10 } \div [ ( 0,4 ) ^ { 9 } \cdot ( 0,4 ) ^ { 7 } \cdot ( 0,4 ) ] =$$

Evaluate

$$0,064$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 10 to get 20.

$$\frac{0,4^{20}}{0,4^{9}\times 0,4^{7}\times 0,4}$$

To multiply powers of the same base, add their exponents. Add 9 and 7 to get 16.

$$\frac{0,4^{20}}{0,4^{16}\times 0,4}$$

To multiply powers of the same base, add their exponents. Add 16 and 1 to get 17.

$$\frac{0,4^{20}}{0,4^{17}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 17 from 20 to get 3.

$$0,4^{3}$$

Calculate 0,4 to the power of 3 and get 0,064.

$$0,064$$

Factor

$$\frac{2 ^ {3}}{5 ^ {3}} = 0.064$$