Solve the Rational Equation for x (2^(x/2))(4^(x/2))=2^6

$(2^{\frac{x}{2}}) (4^{\frac{x}{2}}) = 2^{6}$

Step 1

Multiply $2^{\frac{x}{2}} (4^{\frac{x}{2}})$ .

Rewrite $2^{\frac{x}{2}} (4^{\frac{x}{2}})$ as ${(2 \cdot 4)}^{\frac{x}{2}}$ .

${(2 \cdot 4)}^{\frac{x}{2}} = 2^{6}$

Multiply $2$ by $4$ .

$8^{\frac{x}{2}} = 2^{6}$

Step 2

Raise $2$ to the power of $6$ .

$8^{\frac{x}{2}} = 64$

Step 3

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

$8^{\frac{x}{2}} = 8^{2}$

Step 4

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

$\frac{x}{2} = 2$

Step 5

Solve for $x$ .

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 2$

Rewrite the expression.

$x = 2 \cdot 2$

Simplify the right side.

Multiply $2$ by $2$ .

$x = 4$