Evaluate (49^(5/6))/(49^(1/3))

$\frac{49^{\frac{5}{6}}}{49^{\frac{1}{3}}}$

Step 1

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

$49^{\frac{5}{6}} \cdot 49^{- \frac{1}{3}}$

Step 2

Multiply $49^{\frac{5}{6}}$ by $49^{- \frac{1}{3}}$ by adding the exponents.

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

$49^{\frac{5}{6} - \frac{1}{3}}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$49^{\frac{5}{6} - \frac{1}{3} \cdot \frac{2}{2}}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$49^{\frac{5}{6} - \frac{2}{3 \cdot 2}}$

Multiply $3$ by $2$ .

$49^{\frac{5}{6} - \frac{2}{6}}$

Combine the numerators over the common denominator.

$49^{\frac{5 - 2}{6}}$

Subtract $2$ from $5$ .

$49^{\frac{3}{6}}$

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$49^{\frac{3 (1)}{6}}$

Cancel the common factors.

Factor $3$ out of $6$ .

$49^{\frac{3 \cdot 1}{3 \cdot 2}}$

Cancel the common factor.

$49^{\frac{3 \cdot 1}{3 \cdot 2}}$

Rewrite the expression.

$49^{\frac{1}{2}}$

Step 3

Simplify the expression.

Rewrite $49$ as $7^{2}$ .

${(7^{2})}^{\frac{1}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$7^{2 (\frac{1}{2})}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$7^{2 (\frac{1}{2})}$

Rewrite the expression.

$7^{1}$

Step 5

Evaluate the exponent.

$7$