Solve (sqrt{(-5)^2}+sqrt[3]{(-3)^3})*sqrt{2^frac{1{3}}*2^-frac{7{3}}}

$$( \sqrt { ( - 5 ) ^ { 2 } } + \sqrt[ 3 ] { ( - 3 ) ^ { 3 } } ) \cdot \sqrt { 2 ^ { \frac { 1 } { 3 } } \cdot 2 ^ { - \frac { 7 } { 3 } } }$$

Evaluate

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Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{1}{3} and -\frac{7}{3} to get -2.

$$\left(\sqrt{\left(-5\right)^{2}}+\sqrt[3]{\left(-3\right)^{3}}\right)\sqrt{2^{-2}}$$

Calculate -5 to the power of 2 and get 25.

$$\left(\sqrt{25}+\sqrt[3]{\left(-3\right)^{3}}\right)\sqrt{2^{-2}}$$

Calculate the square root of 25 and get 5.

$$\left(5+\sqrt[3]{\left(-3\right)^{3}}\right)\sqrt{2^{-2}}$$

Calculate -3 to the power of 3 and get -27.

$$\left(5+\sqrt[3]{-27}\right)\sqrt{2^{-2}}$$

Calculate \sqrt[3]{-27} and get -3.

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

Subtract 3 from 5 to get 2.

$$2\sqrt{2^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$2\sqrt{\frac{1}{4}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

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

Multiply 2 and \frac{1}{2} to get 1.

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Factor

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