Simplify (49^(7/2))/(49^(3/2))

$\frac{49^{\frac{7}{2}}}{49^{\frac{3}{2}}}$

Step 1

Move $49^{\frac{3}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$49^{\frac{7}{2}} \cdot 49^{- \frac{3}{2}}$

Step 2

Multiply $49^{\frac{7}{2}}$ by $49^{- \frac{3}{2}}$ by adding the exponents.

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

$49^{\frac{7}{2} - \frac{3}{2}}$

Combine the numerators over the common denominator.

$49^{\frac{7 - 3}{2}}$

Subtract $3$ from $7$ .

$49^{\frac{4}{2}}$

Divide $4$ by $2$ .

$49^{2}$

Step 3

Raise $49$ to the power of $2$ .

$2401$