Solve sqrt{3^2+sqrt{49}}+(1/4)^-1+(2^2)^3

$$\sqrt { 3 ^ { 2 } + \sqrt { 49 } } + ( \frac { 1 } { 4 } ) ^ { - 1 } + ( 2 ^ { 2 } ) ^ { 3 }$$

Evaluate

$$72$$

Solution Steps

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

$$\sqrt{3^{2}+\sqrt{49}}+\left(\frac{1}{4}\right)^{-1}+2^{6}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9+\sqrt{49}}+\left(\frac{1}{4}\right)^{-1}+2^{6}$$

Calculate the square root of 49 and get 7.

$$\sqrt{9+7}+\left(\frac{1}{4}\right)^{-1}+2^{6}$$

Add 9 and 7 to get 16.

$$\sqrt{16}+\left(\frac{1}{4}\right)^{-1}+2^{6}$$

Calculate the square root of 16 and get 4.

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

Calculate \frac{1}{4} to the power of -1 and get 4.

$$4+4+2^{6}$$

Add 4 and 4 to get 8.

$$8+2^{6}$$

Calculate 2 to the power of 6 and get 64.

$$8+64$$

Add 8 and 64 to get 72.

$$72$$

Factor

$$2^{3}\times 3^{2}$$