Solve [(-8)^2+(-2)^5]*[sqrt{144}:(2^3:2^2)]

$$[ ( - 8 ) ^ { 2 } + ( - 2 ) ^ { 5 } ] \cdot [ \sqrt { 144 } : ( 2 ^ { 3 } : 2 ^ { 2 } ) ]$$

Evaluate

$$192$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$\left(\left(-8\right)^{2}+\left(-2\right)^{5}\right)\times \frac{\sqrt{144}}{2^{1}}$$

Calculate -8 to the power of 2 and get 64.

$$\left(64+\left(-2\right)^{5}\right)\times \frac{\sqrt{144}}{2^{1}}$$

Calculate -2 to the power of 5 and get -32.

$$\left(64-32\right)\times \frac{\sqrt{144}}{2^{1}}$$

Subtract 32 from 64 to get 32.

$$32\times \frac{\sqrt{144}}{2^{1}}$$

Calculate the square root of 144 and get 12.

$$32\times \frac{12}{2^{1}}$$

Calculate 2 to the power of 1 and get 2.

$$32\times \frac{12}{2}$$

Divide 12 by 2 to get 6.

$$32\times 6$$

Multiply 32 and 6 to get 192.

$$192$$

Factor

$$2^{6}\times 3$$