Solve [(5/2)*(5/2)^3*(5/2)^-2]^0:(5/2)

$$[ ( \frac { 5 } { 2 } ) \cdot ( \frac { 5 } { 2 } ) ^ { 3 } \cdot ( \frac { 5 } { 2 } ) ^ { - 2 } ] ^ { 0 } : ( \frac { 5 } { 2 } )$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\left(\left(\frac{5}{2}\right)^{4}\times \left(\frac{5}{2}\right)^{-2}\right)^{0}}{\frac{5}{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and -2 to get 2.

$$\frac{\left(\left(\frac{5}{2}\right)^{2}\right)^{0}}{\frac{5}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 0 to get 0.

$$\frac{\left(\frac{5}{2}\right)^{0}}{\frac{5}{2}}$$

Rewrite \frac{5}{2} as \frac{5}{2}\times \left(\frac{5}{2}\right)^{0}. Cancel out \left(\frac{5}{2}\right)^{0} in both numerator and denominator.

$$\frac{1}{\frac{5}{2}}$$

Divide 1 by \frac{5}{2} by multiplying 1 by the reciprocal of \frac{5}{2}.

$$1\times \frac{2}{5}$$

Multiply 1 and \frac{2}{5} to get \frac{2}{5}.

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

Factor

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