Solve sqrt{6}sqrt{2}sqrt{27}+-7^5/-7-11^2

$$\sqrt{ 6 } \sqrt{ 2 } \sqrt{ 27 } + \frac{ { -7 }^{ 5 } }{ -7 } - { 11 }^{ 2 }$$

Evaluate

$$2298$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 5 to get 4.

$$\sqrt{6}\sqrt{2}\sqrt{27}+\left(-7\right)^{4}-11^{2}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$\sqrt{2}\sqrt{3}\sqrt{2}\sqrt{27}+\left(-7\right)^{4}-11^{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\sqrt{3}\sqrt{27}+\left(-7\right)^{4}-11^{2}$$

Factor 27=3\times 9. Rewrite the square root of the product \sqrt{3\times 9} as the product of square roots \sqrt{3}\sqrt{9}.

$$2\sqrt{3}\sqrt{3}\sqrt{9}+\left(-7\right)^{4}-11^{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\times 3\sqrt{9}+\left(-7\right)^{4}-11^{2}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{9}+\left(-7\right)^{4}-11^{2}$$

Calculate the square root of 9 and get 3.

$$6\times 3+\left(-7\right)^{4}-11^{2}$$

Multiply 6 and 3 to get 18.

$$18+\left(-7\right)^{4}-11^{2}$$

Calculate -7 to the power of 4 and get 2401.

$$18+2401-11^{2}$$

Add 18 and 2401 to get 2419.

$$2419-11^{2}$$

Calculate 11 to the power of 2 and get 121.

$$2419-121$$

Subtract 121 from 2419 to get 2298.

$$2298$$

Factor

$$2\times 3\times 383$$