Simplify (x^(5/3)y^-2)^0

${(x^{\frac{5}{3}} y^{- 2})}^{0}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(x^{\frac{5}{3}} \frac{1}{y^{2}})}^{0}$

Step 2

Combine fractions.

Combine $x^{\frac{5}{3}}$ and $\frac{1}{y^{2}}$ .

${(\frac{x^{\frac{5}{3}}}{y^{2}})}^{0}$

Apply the product rule to $\frac{x^{\frac{5}{3}}}{y^{2}}$ .

$\frac{{(x^{\frac{5}{3}})}^{0}}{{(y^{2})}^{0}}$

Step 3

Simplify the numerator.

Multiply the exponents in ${(x^{\frac{5}{3}})}^{0}$ .

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

$\frac{x^{\frac{5}{3} \cdot 0}}{{(y^{2})}^{0}}$

Multiply $\frac{5}{3}$ by $0$ .

$\frac{x^{0}}{{(y^{2})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1}{{(y^{2})}^{0}}$

Step 4

Simplify the denominator.

Multiply the exponents in ${(y^{2})}^{0}$ .

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

$\frac{1}{y^{2 \cdot 0}}$

Multiply $2$ by $0$ .

$\frac{1}{y^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 5

Divide $1$ by $1$ .

$1$