Simplify ((34^3)/(3^-24^-7))^0

${(\frac{3 \cdot 4^{3}}{3^{- 2} \cdot 4^{- 7}})}^{0}$

Step 1

Move $3^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{3 \cdot 4^{3} \cdot 3^{2}}{4^{- 7}})}^{0}$

Step 2

Move $4^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(3 \cdot 4^{3} \cdot 3^{2} \cdot 4^{7})}^{0}$

Step 3

Multiply $3$ by $3^{2}$ by adding the exponents.

Move $3^{2}$ .

${(3^{2} \cdot 3 \cdot 4^{3} \cdot 4^{7})}^{0}$

Multiply $3^{2}$ by $3$ .

Raise $3$ to the power of $1$ .

${(3^{2} \cdot 3^{1} \cdot 4^{3} \cdot 4^{7})}^{0}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(3^{2 + 1} \cdot 4^{3} \cdot 4^{7})}^{0}$

Add $2$ and $1$ .

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

Step 4

Multiply $4^{3}$ by $4^{7}$ by adding the exponents.

Move $4^{7}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(3^{3} \cdot 4^{7 + 3})}^{0}$

Add $7$ and $3$ .

${(3^{3} \cdot 4^{10})}^{0}$

Step 5

Raise $3$ to the power of $3$ .

${(27 \cdot 4^{10})}^{0}$

Step 6

Raise $4$ to the power of $10$ .

${(27 \cdot 1048576)}^{0}$

Step 7

Multiply $27$ by $1048576$ .

$28311552^{0}$

Step 8

Anything raised to $0$ is $1$ .

$1$

Simplify ((3*4^3)/(3^-2*4^-7))^0