Simplify 27^(1/3)-16^(1/4)-4^(1/2)

$27^{\frac{1}{3}} - 16^{\frac{1}{4}} - 4^{\frac{1}{2}}$

Simplify each term.

Rewrite $27$ as $3^{3}$ .

${(3^{3})}^{\frac{1}{3}} - 16^{\frac{1}{4}} - 4^{\frac{1}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{3 (\frac{1}{3})} - 16^{\frac{1}{4}} - 4^{\frac{1}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$3^{3 (\frac{1}{3})} - 16^{\frac{1}{4}} - 4^{\frac{1}{2}}$

Rewrite the expression.

$3^{1} - 16^{\frac{1}{4}} - 4^{\frac{1}{2}}$

Evaluate the exponent.

$3 - 16^{\frac{1}{4}} - 4^{\frac{1}{2}}$

Rewrite $16$ as $2^{4}$ .

$3 - {(2^{4})}^{\frac{1}{4}} - 4^{\frac{1}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 - 2^{4 (\frac{1}{4})} - 4^{\frac{1}{2}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$3 - 2^{4 (\frac{1}{4})} - 4^{\frac{1}{2}}$

Rewrite the expression.

$3 - 2^{1} - 4^{\frac{1}{2}}$

Evaluate the exponent.

$3 - 1 \cdot 2 - 4^{\frac{1}{2}}$

Multiply $- 1$ by $2$ .

$3 - 2 - 4^{\frac{1}{2}}$

Rewrite $4$ as $2^{2}$ .

$3 - 2 - {(2^{2})}^{\frac{1}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 - 2 - 2^{2 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 - 2 - 2^{2 (\frac{1}{2})}$

Rewrite the expression.

$3 - 2 - 2^{1}$

Evaluate the exponent.

$3 - 2 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$3 - 2 - 2$

Simplify by subtracting numbers.

Subtract $2$ from $3$ .

$1 - 2$

Subtract $2$ from $1$ .

$- 1$