Solve 10:(21/3+sqrt{(-4)^2})^-1+53/3]^1/2*(4^-3/2+5/24)

$$10 : ( 2 \frac { 1 } { 3 } + \sqrt { ( - 4 ) ^ { 2 } } ) ^ { - 1 } + \frac { 53 } { 3 } ] ^ { 1 / 2 } \cdot ( 4 ^ { - 3 / 2 } + \frac { 5 } { 24 } )$$

Evaluate

$$81$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{10}{\left(\frac{6+1}{3}+\sqrt{\left(-4\right)^{2}}\right)^{-1}}+\frac{53}{3}$$

Add 6 and 1 to get 7.

$$\frac{10}{\left(\frac{7}{3}+\sqrt{\left(-4\right)^{2}}\right)^{-1}}+\frac{53}{3}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{10}{\left(\frac{7}{3}+\sqrt{16}\right)^{-1}}+\frac{53}{3}$$

Calculate the square root of 16 and get 4.

$$\frac{10}{\left(\frac{7}{3}+4\right)^{-1}}+\frac{53}{3}$$

Add \frac{7}{3} and 4 to get \frac{19}{3}.

$$\frac{10}{\left(\frac{19}{3}\right)^{-1}}+\frac{53}{3}$$

Calculate \frac{19}{3} to the power of -1 and get \frac{3}{19}.

$$\frac{10}{\frac{3}{19}}+\frac{53}{3}$$

Divide 10 by \frac{3}{19} by multiplying 10 by the reciprocal of \frac{3}{19}.

$$10\times \frac{19}{3}+\frac{53}{3}$$

Multiply 10 and \frac{19}{3} to get \frac{190}{3}.

$$\frac{190}{3}+\frac{53}{3}$$

Add \frac{190}{3} and \frac{53}{3} to get 81.

$$81$$

Factor

$$3^{4}$$