Solve [(5/2)^-5]^-3:[(5/2)^2]^4:(5/2)

$$[ ( \frac { 5 } { 2 } ) ^ { - 5 } ] ^ { - 3 } : [ ( \frac { 5 } { 2 } ) ^ { 2 } ] ^ { 4 } : ( \frac { 5 } { 2 } )$$

Evaluate

$$\frac{15625}{64}=244.140625$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\frac{\frac{\left(\frac{5}{2}\right)^{15}}{\left(\left(\frac{5}{2}\right)^{2}\right)^{4}}}{\frac{5}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{\frac{\left(\frac{5}{2}\right)^{15}}{\left(\frac{5}{2}\right)^{8}}}{\frac{5}{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 8 from 15 to get 7.

$$\frac{\left(\frac{5}{2}\right)^{7}}{\frac{5}{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 7 to get 6.

$$\left(\frac{5}{2}\right)^{6}$$

Calculate \frac{5}{2} to the power of 6 and get \frac{15625}{64}.

$$\frac{15625}{64}$$

Factor

$$\frac{5 ^ {6}}{2 ^ {6}} = 244\frac{9}{64} = 244.140625$$