Solve for k 64^(1/k)=2

$64^{\frac{1}{k}} = 2$

Create equivalent expressions in the equation that all have equal bases.

$2^{6 \frac{1}{k}} = 2^{1}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$6 \frac{1}{k} = 1$

Solve for $k$ .

Combine $6$ and $\frac{1}{k}$ .

$\frac{6}{k} = 1$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$k, 1$

The LCM of one and any expression is the expression.

$k$

Multiply each term in $\frac{6}{k} = 1$ by $k$ to eliminate the fractions.

Multiply each term in $\frac{6}{k} = 1$ by $k$ .

$\frac{6}{k} k = 1 k$

Simplify the left side.

Cancel the common factor of $k$ .

Cancel the common factor.

$\frac{6}{k} k = 1 k$

Rewrite the expression.

$6 = 1 k$

Simplify the right side.

Multiply $k$ by $1$ .

$6 = k$

Rewrite the equation as $k = 6$ .

$k = 6$