Solve 5^4left(5^-2right)^-32^3/{5^3{10}^2{5}^6}

$$\frac{ { 5 }^{ 4 } { \left( { 5 }^{ -2 } \right) }^{ -3 } { 2 }^{ 3 } }{ { 5 }^{ 3 } { 10 }^{ 2 } { 5 }^{ 6 } }$$

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$\frac{5^{4}\times 5^{6}\times 2^{3}}{5^{3}\times 10^{2}\times 5^{6}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{5^{10}\times 2^{3}}{5^{3}\times 10^{2}\times 5^{6}}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{5^{10}\times 2^{3}}{5^{9}\times 10^{2}}$$

Cancel out 5^{9} in both numerator and denominator.

$$\frac{5\times 2^{3}}{10^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{5\times 8}{10^{2}}$$

Multiply 5 and 8 to get 40.

$$\frac{40}{10^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{40}{100}$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$