Solve for k 64^(1/3)=2^k

$64^{\frac{1}{3}} = 2^{k}$

Step 1

Rewrite the equation as $2^{k} = 64^{\frac{1}{3}}$ .

$2^{k} = 64^{\frac{1}{3}}$

Step 2

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

$2^{k} = 2^{6 (\frac{1}{3})}$

Step 3

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

$k = 6 (\frac{1}{3})$

Step 4

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$k = 3 (2) \frac{1}{3}$

Cancel the common factor.

$k = 3 \cdot 2 \frac{1}{3}$

Rewrite the expression.

$k = 2$