Solve sqrt[3]{frac{11^56/36^211^2}}{sqrt{{left(-2/9right)}^2}}+{left(2^15/{2^12}right)}^2{2}^-2

$$\frac{ \sqrt[ 3 ]{ \frac{ { 11 }^{ 5 } 6 }{ { 36 }^{ 2 } { 11 }^{ 2 } } } }{ \sqrt{ { \left(- \frac{ 2 }{ 9 } \right) }^{ 2 } } } + { \left( \frac{ { 2 }^{ 15 } }{ { 2 }^{ 12 } } \right) }^{ 2 } { 2 }^{ -2 }$$

Evaluate

$$\frac{97}{4}=24.25$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 15 to get 3.

$$\frac{\sqrt[3]{\frac{11^{5}\times 6}{36^{2}\times 11^{2}}}}{\sqrt{\left(-\frac{2}{9}\right)^{2}}}+\left(2^{3}\right)^{2}\times 2^{-2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\sqrt[3]{\frac{11^{5}\times 6}{36^{2}\times 11^{2}}}}{\sqrt{\left(-\frac{2}{9}\right)^{2}}}+2^{6}\times 2^{-2}$$

To multiply powers of the same base, add their exponents. Add 6 and -2 to get 4.

$$\frac{\sqrt[3]{\frac{11^{5}\times 6}{36^{2}\times 11^{2}}}}{\sqrt{\left(-\frac{2}{9}\right)^{2}}}+2^{4}$$

Cancel out 11^{2} in both numerator and denominator.

$$\frac{\sqrt[3]{\frac{6\times 11^{3}}{36^{2}}}}{\sqrt{\left(-\frac{2}{9}\right)^{2}}}+2^{4}$$

Calculate 11 to the power of 3 and get 1331.

$$\frac{\sqrt[3]{\frac{6\times 1331}{36^{2}}}}{\sqrt{\left(-\frac{2}{9}\right)^{2}}}+2^{4}$$

Multiply 6 and 1331 to get 7986.

$$\frac{\sqrt[3]{\frac{7986}{36^{2}}}}{\sqrt{\left(-\frac{2}{9}\right)^{2}}}+2^{4}$$

Calculate 36 to the power of 2 and get 1296.

$$\frac{\sqrt[3]{\frac{7986}{1296}}}{\sqrt{\left(-\frac{2}{9}\right)^{2}}}+2^{4}$$

Reduce the fraction \frac{7986}{1296} to lowest terms by extracting and canceling out 6.

$$\frac{\sqrt[3]{\frac{1331}{216}}}{\sqrt{\left(-\frac{2}{9}\right)^{2}}}+2^{4}$$

Calculate \sqrt[3]{\frac{1331}{216}} and get \frac{11}{6}.

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

Calculate -\frac{2}{9} to the power of 2 and get \frac{4}{81}.

$$\frac{\frac{11}{6}}{\sqrt{\frac{4}{81}}}+2^{4}$$

Rewrite the square root of the division \frac{4}{81} as the division of square roots \frac{\sqrt{4}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{\frac{11}{6}}{\frac{2}{9}}+2^{4}$$

Divide \frac{11}{6} by \frac{2}{9} by multiplying \frac{11}{6} by the reciprocal of \frac{2}{9}.

$$\frac{11}{6}\times \frac{9}{2}+2^{4}$$

Multiply \frac{11}{6} and \frac{9}{2} to get \frac{33}{4}.

$$\frac{33}{4}+2^{4}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{33}{4}+16$$

Add \frac{33}{4} and 16 to get \frac{97}{4}.

$$\frac{97}{4}$$

Factor

$$\frac{97}{2 ^ {2}} = 24\frac{1}{4} = 24.25$$