Evaluate (49^(3/8)*49^(7/8))/(7^(5/4))

$\frac{49^{\frac{3}{8}} \cdot 49^{\frac{7}{8}}}{7^{\frac{5}{4}}}$

Step 1

Multiply $49^{\frac{3}{8}}$ by $49^{\frac{7}{8}}$ by adding the exponents.

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

$\frac{49^{\frac{3}{8} + \frac{7}{8}}}{7^{\frac{5}{4}}}$

Combine the numerators over the common denominator.

$\frac{49^{\frac{3 + 7}{8}}}{7^{\frac{5}{4}}}$

Add $3$ and $7$ .

$\frac{49^{\frac{10}{8}}}{7^{\frac{5}{4}}}$

Cancel the common factor of $10$ and $8$ .

Factor $2$ out of $10$ .

$\frac{49^{\frac{2 (5)}{8}}}{7^{\frac{5}{4}}}$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{49^{\frac{2 \cdot 5}{2 \cdot 4}}}{7^{\frac{5}{4}}}$

Cancel the common factor.

$\frac{49^{\frac{2 \cdot 5}{2 \cdot 4}}}{7^{\frac{5}{4}}}$

Rewrite the expression.

$\frac{49^{\frac{5}{4}}}{7^{\frac{5}{4}}}$

Step 2

Use the power of quotient rule $\frac{a^{m}}{b^{m}} = {(\frac{a}{b})}^{m}$ .

${(\frac{49}{7})}^{\frac{5}{4}}$

Step 3

Divide $49$ by $7$ .

$7^{\frac{5}{4}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$7^{\frac{5}{4}}$

Decimal Form:

$11.38603593 \dots$