Solve 2^7:2^5-sqrt{10^2-7*(-3)+(-7+5)}=

$$2 ^ { 7 } : 2 ^ { 5 } - \sqrt { 10 ^ { 2 } - 7 \cdot ( - 3 ) + ( - 7 + 5 ) } =$$

Evaluate

$$4-\sqrt{119}\approx -6.908712115$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 to get 2.

$$2^{2}-\sqrt{10^{2}-7\left(-3\right)-7+5}$$

Calculate 2 to the power of 2 and get 4.

$$4-\sqrt{10^{2}-7\left(-3\right)-7+5}$$

Calculate 10 to the power of 2 and get 100.

$$4-\sqrt{100-7\left(-3\right)-7+5}$$

Multiply 7 and -3 to get -21.

$$4-\sqrt{100-\left(-21\right)-7+5}$$

The opposite of -21 is 21.

$$4-\sqrt{100+21-7+5}$$

Add 100 and 21 to get 121.

$$4-\sqrt{121-7+5}$$

Subtract 7 from 121 to get 114.

$$4-\sqrt{114+5}$$

Add 114 and 5 to get 119.

$$4-\sqrt{119}$$