Question

evaluate the expression.
\left(49^{\frac{1}{3}}\
ight)\left(49^{\frac{1}{6}}\
ight)
\left(49^{\frac{1}{3}}\
ight)\left(49^{\frac{1}{6}}\
ight) = \square

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$
$49^{\frac{1}{3}} \cdot 49^{\frac{1}{6}} = 49^{\frac{1}{3}+\frac{1}{6}}$

Step2: Add the fractions

Find a common denominator to add the exponents.
$\frac{1}{3}+\frac{1}{6} = \frac{2}{6}+\frac{1}{6} = \frac{3}{6} = \frac{1}{2}$

Step3: Simplify the exponential term

Rewrite 49 as a perfect square and evaluate the exponent.
$49^{\frac{1}{2}} = \sqrt{49} = 7$

Answer:

7