Simplify (2^35^42^-15^2)/(5^32^-25^32^4)

$\frac{2^{3} \cdot 5^{4} \cdot 2^{- 1} \cdot 5^{2}}{5^{3} \cdot 2^{- 2} \cdot 5^{3} \cdot 2^{4}}$

Step 1

Multiply $2^{3}$ by $2^{- 1}$ by adding the exponents.

Move $2^{- 1}$ .

$\frac{2^{- 1} \cdot 2^{3} \cdot 5^{4} \cdot 5^{2}}{5^{3} \cdot 2^{- 2} \cdot 5^{3} \cdot 2^{4}}$

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

$\frac{2^{- 1 + 3} \cdot 5^{4} \cdot 5^{2}}{5^{3} \cdot 2^{- 2} \cdot 5^{3} \cdot 2^{4}}$

Add $- 1$ and $3$ .

$\frac{2^{2} \cdot 5^{4} \cdot 5^{2}}{5^{3} \cdot 2^{- 2} \cdot 5^{3} \cdot 2^{4}}$

Step 2

Multiply $5^{4}$ by $5^{2}$ by adding the exponents.

Move $5^{2}$ .

$\frac{2^{2} \cdot (5^{2} \cdot 5^{4})}{5^{3} \cdot 2^{- 2} \cdot 5^{3} \cdot 2^{4}}$

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

$\frac{2^{2} \cdot 5^{2 + 4}}{5^{3} \cdot 2^{- 2} \cdot 5^{3} \cdot 2^{4}}$

Add $2$ and $4$ .

$\frac{2^{2} \cdot 5^{6}}{5^{3} \cdot 2^{- 2} \cdot 5^{3} \cdot 2^{4}}$

Step 3

Multiply $5^{3}$ by $5^{3}$ by adding the exponents.

Move $5^{3}$ .

$\frac{2^{2} \cdot 5^{6}}{5^{3} \cdot 5^{3} \cdot 2^{- 2} \cdot 2^{4}}$

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

$\frac{2^{2} \cdot 5^{6}}{5^{3 + 3} \cdot 2^{- 2} \cdot 2^{4}}$

Add $3$ and $3$ .

$\frac{2^{2} \cdot 5^{6}}{5^{6} \cdot 2^{- 2} \cdot 2^{4}}$

Step 4

Multiply $2^{- 2}$ by $2^{4}$ by adding the exponents.

Move $2^{4}$ .

$\frac{2^{2} \cdot 5^{6}}{5^{6} \cdot (2^{4} \cdot 2^{- 2})}$

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

$\frac{2^{2} \cdot 5^{6}}{5^{6} \cdot 2^{4 - 2}}$

Subtract $2$ from $4$ .

$\frac{2^{2} \cdot 5^{6}}{5^{6} \cdot 2^{2}}$

Step 5

Cancel the common factor of $2^{2}$ .

Cancel the common factor.

$\frac{2^{2} \cdot 5^{6}}{5^{6} \cdot 2^{2}}$

Rewrite the expression.

$\frac{5^{6}}{5^{6}}$

Step 6

Cancel the common factor of $5^{6}$ .

Cancel the common factor.

$\frac{5^{6}}{5^{6}}$

Rewrite the expression.

$1$

Simplify (2^3*5^4*2^-1*5^2)/(5^3*2^-2*5^3*2^4)

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Simplify (2^35^42^-15^2)/(5^32^-25^32^4)