Simplify (2^(1/3)*2^-3)^0

${(2^{\frac{1}{3}} \cdot 2^{- 3})}^{0}$

Step 1

Multiply $2^{\frac{1}{3}}$ by $2^{- 3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(2^{\frac{1}{3} - 3})}^{0}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(2^{\frac{1}{3} - 3 \cdot \frac{3}{3}})}^{0}$

Combine $- 3$ and $\frac{3}{3}$ .

${(2^{\frac{1}{3} + \frac{- 3 \cdot 3}{3}})}^{0}$

Combine the numerators over the common denominator.

${(2^{\frac{1 - 3 \cdot 3}{3}})}^{0}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

${(2^{\frac{1 - 9}{3}})}^{0}$

Subtract $9$ from $1$ .

${(2^{\frac{- 8}{3}})}^{0}$

Move the negative in front of the fraction.

${(2^{- \frac{8}{3}})}^{0}$

Step 2

Multiply the exponents in ${(2^{- \frac{8}{3}})}^{0}$ .

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

$2^{- \frac{8}{3} \cdot 0}$

Multiply $- \frac{8}{3} \cdot 0$ .

Multiply $0$ by $- 1$ .

$2^{0 (\frac{8}{3})}$

Multiply $0$ by $\frac{8}{3}$ .

$2^{0}$

Step 3

Anything raised to $0$ is $1$ .

$1$