Evaluate (7(5)^(5/3))/(49(5)^(2/3))

$\frac{7 {(5)}^{\frac{5}{3}}}{49 {(5)}^{\frac{2}{3}}}$

Move ${(5)}^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{7 {(5)}^{\frac{5}{3}} \cdot 5^{- \frac{2}{3}}}{49}$

Simplify the numerator.

Multiply ${(5)}^{\frac{5}{3}}$ by $5^{- \frac{2}{3}}$ by adding the exponents.

Move $5^{- \frac{2}{3}}$ .

$\frac{7 (5^{- \frac{2}{3}} {(5)}^{\frac{5}{3}})}{49}$

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

$\frac{7 \cdot 5^{- \frac{2}{3} + \frac{5}{3}}}{49}$

Combine the numerators over the common denominator.

$\frac{7 \cdot 5^{\frac{- 2 + 5}{3}}}{49}$

Add $- 2$ and $5$ .

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

Divide $3$ by $3$ .

$\frac{7 \cdot 5^{1}}{49}$

Simplify $7 \cdot 5^{1}$ .

$\frac{7 \cdot 5}{49}$

Cancel the common factor of $7$ and $49$ .

Factor $7$ out of $7 \cdot 5$ .

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

Cancel the common factors.

Factor $7$ out of $49$ .

$\frac{7 \cdot 5}{7 \cdot 7}$

Cancel the common factor.

$\frac{7 \cdot 5}{7 \cdot 7}$

Rewrite the expression.

$\frac{5}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{7}$

Decimal Form:

$0.\overline{714285}$