Simplify 6+1.5(5x^(3/5)y^(2/3))^0

$6 + 1.5 {(5 x^{\frac{3}{5}} y^{\frac{2}{3}})}^{0}$

Step 1

Simplify each term.

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

$6 + 1.5 ({(5 x^{\frac{3}{5}})}^{0} {(y^{\frac{2}{3}})}^{0})$

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

$6 + 1.5 (5^{0} {(x^{\frac{3}{5}})}^{0} {(y^{\frac{2}{3}})}^{0})$

Anything raised to $0$ is $1$ .

$6 + 1.5 (1 {(x^{\frac{3}{5}})}^{0} {(y^{\frac{2}{3}})}^{0})$

Multiply ${(x^{\frac{3}{5}})}^{0}$ by $1$ .

$6 + 1.5 ({(x^{\frac{3}{5}})}^{0} {(y^{\frac{2}{3}})}^{0})$

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

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

$6 + 1.5 (x^{\frac{3}{5} \cdot 0} {(y^{\frac{2}{3}})}^{0})$

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

$6 + 1.5 (x^{0} {(y^{\frac{2}{3}})}^{0})$

Anything raised to $0$ is $1$ .

$6 + 1.5 (1 {(y^{\frac{2}{3}})}^{0})$

Multiply ${(y^{\frac{2}{3}})}^{0}$ by $1$ .

$6 + 1.5 {(y^{\frac{2}{3}})}^{0}$

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

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

$6 + 1.5 y^{\frac{2}{3} \cdot 0}$

Multiply $\frac{2}{3}$ by $0$ .

$6 + 1.5 y^{0}$

Anything raised to $0$ is $1$ .

$6 + 1.5 \cdot 1$

Multiply $1.5$ by $1$ .

$6 + 1.5$

Step 2

Add $6$ and $1.5$ .

$7.5$