Simplify (34x^5y^6z^-7)^0

${(34 x^{5} y^{6} z^{- 7})}^{0}$

Step 1

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

${(34 x^{5} y^{6} \frac{1}{z^{7}})}^{0}$

Step 2

Multiply $34 x^{5} y^{6} \frac{1}{z^{7}}$ .

Combine $34$ and $\frac{1}{z^{7}}$ .

${(x^{5} y^{6} \frac{34}{z^{7}})}^{0}$

Combine $x^{5}$ and $\frac{34}{z^{7}}$ .

${(y^{6} \frac{x^{5} \cdot 34}{z^{7}})}^{0}$

Combine $y^{6}$ and $\frac{x^{5} \cdot 34}{z^{7}}$ .

${(\frac{y^{6} (x^{5} \cdot 34)}{z^{7}})}^{0}$

Step 3

Move $34$ to the left of $y^{6} x^{5}$ .

${(\frac{34 \cdot (y^{6} x^{5})}{z^{7}})}^{0}$

Step 4

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

Apply the product rule to $\frac{34 y^{6} x^{5}}{z^{7}}$ .

$\frac{{(34 y^{6} x^{5})}^{0}}{{(z^{7})}^{0}}$

Apply the product rule to $34 y^{6} x^{5}$ .

$\frac{{(34 y^{6})}^{0} {(x^{5})}^{0}}{{(z^{7})}^{0}}$

Apply the product rule to $34 y^{6}$ .

$\frac{34^{0} {(y^{6})}^{0} {(x^{5})}^{0}}{{(z^{7})}^{0}}$

Step 5

Simplify the numerator.

Anything raised to $0$ is $1$ .

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

Multiply the exponents in ${(y^{6})}^{0}$ .

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

$\frac{1 y^{6 \cdot 0} {(x^{5})}^{0}}{{(z^{7})}^{0}}$

Multiply $6$ by $0$ .

$\frac{1 y^{0} {(x^{5})}^{0}}{{(z^{7})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1 {(x^{5})}^{0}}{{(z^{7})}^{0}}$

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

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

$\frac{1 \cdot 1 x^{5 \cdot 0}}{{(z^{7})}^{0}}$

Multiply $5$ by $0$ .

$\frac{1 \cdot 1 x^{0}}{{(z^{7})}^{0}}$

Anything raised to $0$ is $1$ .

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

Combine exponents.

Multiply $1$ by $1$ .

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

Multiply $1$ by $1$ .

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

Step 6

Simplify the denominator.

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

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

$\frac{1}{z^{7 \cdot 0}}$

Multiply $7$ by $0$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 7

Divide $1$ by $1$ .

$1$

Simplify (34x^5y^6z^-7)^0

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