Simplify ((9a^3b^7)^4)^0

${({(9 a^{3} b^{7})}^{4})}^{0}$

Step 1

Multiply the exponents in ${({(9 a^{3} b^{7})}^{4})}^{0}$ .

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

${(9 a^{3} b^{7})}^{4 \cdot 0}$

Multiply $4$ by $0$ .

${(9 a^{3} b^{7})}^{0}$

Step 2

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

Apply the product rule to $9 a^{3} b^{7}$ .

${(9 a^{3})}^{0} {(b^{7})}^{0}$

Apply the product rule to $9 a^{3}$ .

$9^{0} {(a^{3})}^{0} {(b^{7})}^{0}$

Step 3

Anything raised to $0$ is $1$ .

$1 {(a^{3})}^{0} {(b^{7})}^{0}$

Step 4

Multiply ${(a^{3})}^{0}$ by $1$ .

${(a^{3})}^{0} {(b^{7})}^{0}$

Step 5

Multiply the exponents in ${(a^{3})}^{0}$ .

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

$a^{3 \cdot 0} {(b^{7})}^{0}$

Multiply $3$ by $0$ .

$a^{0} {(b^{7})}^{0}$

Step 6

Anything raised to $0$ is $1$ .

$1 {(b^{7})}^{0}$

Step 7

Multiply ${(b^{7})}^{0}$ by $1$ .

${(b^{7})}^{0}$

Step 8

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

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

$b^{7 \cdot 0}$

Multiply $7$ by $0$ .

$b^{0}$

Step 9

Anything raised to $0$ is $1$ .

$1$