Solve 3sqrt[3]{4^2*4}*sqrt[3]{(-5)^3}+sqrt{16}-sqrt[3]{16}

$$3 \sqrt[ 3 ] { 4 ^ { 2 } \times 4 } \times \sqrt[ 3 ] { ( - 5 ) ^ { 3 } } + \sqrt { 16 } - \sqrt[ 3 ] { 16 }$$

Evaluate

$$-2^{\frac{4}{3}}-56\approx -58.5198421$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$3\sqrt[3]{4^{3}}\sqrt[3]{\left(-5\right)^{3}}+\sqrt{16}-\sqrt[3]{16}$$

Calculate 4 to the power of 3 and get 64.

$$3\sqrt[3]{64}\sqrt[3]{\left(-5\right)^{3}}+\sqrt{16}-\sqrt[3]{16}$$

Calculate \sqrt[3]{64} and get 4.

$$3\times 4\sqrt[3]{\left(-5\right)^{3}}+\sqrt{16}-\sqrt[3]{16}$$

Multiply 3 and 4 to get 12.

$$12\sqrt[3]{\left(-5\right)^{3}}+\sqrt{16}-\sqrt[3]{16}$$

Calculate -5 to the power of 3 and get -125.

$$12\sqrt[3]{-125}+\sqrt{16}-\sqrt[3]{16}$$

Calculate \sqrt[3]{-125} and get -5.

$$12\left(-5\right)+\sqrt{16}-\sqrt[3]{16}$$

Multiply 12 and -5 to get -60.

$$-60+\sqrt{16}-\sqrt[3]{16}$$

Calculate the square root of 16 and get 4.

$$-60+4-\sqrt[3]{16}$$

Add -60 and 4 to get -56.

$$-56-\sqrt[3]{16}$$