Solve [(-8)^3:(-2)^9]*[sqrt{144}:(2^7:2^5)]

$$[ ( - 8 ) ^ { 3 } : ( - 2 ) ^ { 9 } ] \cdot [ \sqrt { 144 } : ( 2 ^ { 7 } : 2 ^ { 5 } ) ]$$

Evaluate

$$3$$

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.

$$\frac{\left(-8\right)^{3}}{\left(-2\right)^{9}}\times \frac{\sqrt{144}}{2^{2}}$$

Calculate -8 to the power of 3 and get -512.

$$\frac{-512}{\left(-2\right)^{9}}\times \frac{\sqrt{144}}{2^{2}}$$

Calculate -2 to the power of 9 and get -512.

$$\frac{-512}{-512}\times \frac{\sqrt{144}}{2^{2}}$$

Divide -512 by -512 to get 1.

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

Calculate the square root of 144 and get 12.

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

Calculate 2 to the power of 2 and get 4.

$$1\times \frac{12}{4}$$

Divide 12 by 4 to get 3.

$$1\times 3$$

Multiply 1 and 3 to get 3.

$$3$$

Factor

$$3$$