Solve sqrt{2^10}2^52^5sqrt[3]{2^25}div1024

$$\sqrt{ { 2 }^{ 10 } } { 2 }^{ 5 } { 2 }^{ 5 } \sqrt[ 3 ]{ { 2 }^{ 25 } } \div 1024$$

Evaluate

$$8192\sqrt[3]{2}\approx 10321.273240739$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{\sqrt{2^{10}}\times 2^{10}\sqrt[3]{2^{25}}}{1024}$$

Calculate 2 to the power of 10 and get 1024.

$$\frac{\sqrt{1024}\times 2^{10}\sqrt[3]{2^{25}}}{1024}$$

Calculate the square root of 1024 and get 32.

$$\frac{32\times 2^{10}\sqrt[3]{2^{25}}}{1024}$$

Calculate 2 to the power of 10 and get 1024.

$$\frac{32\times 1024\sqrt[3]{2^{25}}}{1024}$$

Multiply 32 and 1024 to get 32768.

$$\frac{32768\sqrt[3]{2^{25}}}{1024}$$

Calculate 2 to the power of 25 and get 33554432.

$$\frac{32768\sqrt[3]{33554432}}{1024}$$

Divide 32768\sqrt[3]{33554432} by 1024 to get 32\sqrt[3]{33554432}.

$$32\sqrt[3]{33554432}$$