Simplify 8.12(x^(2/3)y^(4/5)z^(6/7))^0

$8.12 {(x^{\frac{2}{3}} y^{\frac{4}{5}} z^{\frac{6}{7}})}^{0}$

Step 1

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

Apply the product rule to $x^{\frac{2}{3}} y^{\frac{4}{5}} z^{\frac{6}{7}}$ .

$8.12 ({(x^{\frac{2}{3}} y^{\frac{4}{5}})}^{0} {(z^{\frac{6}{7}})}^{0})$

Apply the product rule to $x^{\frac{2}{3}} y^{\frac{4}{5}}$ .

$8.12 ({(x^{\frac{2}{3}})}^{0} {(y^{\frac{4}{5}})}^{0} {(z^{\frac{6}{7}})}^{0})$

Step 2

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

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

$8.12 (x^{\frac{2}{3} \cdot 0} {(y^{\frac{4}{5}})}^{0} {(z^{\frac{6}{7}})}^{0})$

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

$8.12 (x^{0} {(y^{\frac{4}{5}})}^{0} {(z^{\frac{6}{7}})}^{0})$

Step 3

Anything raised to $0$ is $1$ .

$8.12 (1 {(y^{\frac{4}{5}})}^{0} {(z^{\frac{6}{7}})}^{0})$

Step 4

Multiply ${(y^{\frac{4}{5}})}^{0}$ by $1$ .

$8.12 ({(y^{\frac{4}{5}})}^{0} {(z^{\frac{6}{7}})}^{0})$

Step 5

Multiply the exponents in ${(y^{\frac{4}{5}})}^{0}$ .

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

$8.12 (y^{\frac{4}{5} \cdot 0} {(z^{\frac{6}{7}})}^{0})$

Multiply $\frac{4}{5}$ by $0$ .

$8.12 (y^{0} {(z^{\frac{6}{7}})}^{0})$

Step 6

Anything raised to $0$ is $1$ .

$8.12 (1 {(z^{\frac{6}{7}})}^{0})$

Step 7

Multiply ${(z^{\frac{6}{7}})}^{0}$ by $1$ .

$8.12 {(z^{\frac{6}{7}})}^{0}$

Step 8

Multiply the exponents in ${(z^{\frac{6}{7}})}^{0}$ .

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

$8.12 z^{\frac{6}{7} \cdot 0}$

Multiply $\frac{6}{7}$ by $0$ .

$8.12 z^{0}$

Step 9

Anything raised to $0$ is $1$ .

$8.12 \cdot 1$

Step 10

Multiply $8.12$ by $1$ .

$8.12$