Solve for x 64*4^(3x)=16

$64 \cdot 4^{3 x} = 16$

Rewrite $64$ as $2^{6}$ .

$2^{6} \cdot 4^{3 x} = 16$

Rewrite $4$ as $2^{2}$ .

$2^{6} \cdot {(2^{2})}^{3 x} = 16$

Multiply the exponents in ${(2^{2})}^{3 x}$ .

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

$2^{6} \cdot 2^{2 (3 x)} = 16$

Multiply $3$ by $2$ .

$2^{6} \cdot 2^{6 x} = 16$

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

$2^{6 + 6 x} = 16$

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

$2^{6 + 6 x} = 2^{4}$

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

$6 + 6 x = 4$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$6 x = 4 - 6$

Subtract $6$ from $4$ .

$6 x = - 2$

Divide each term in $6 x = - 2$ by $6$ and simplify.

Divide each term in $6 x = - 2$ by $6$ .

$\frac{6 x}{6} = \frac{- 2}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 2}{6}$

Divide $x$ by $1$ .

$x = \frac{- 2}{6}$

Simplify the right side.

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2$ .

$x = \frac{2 (- 1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 \cdot - 1}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 \cdot - 1}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{- 1}{3}$

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{3}$

Decimal Form:

$x = - 0.\overline{3}$

Solve for x 64*4^(3x)=16

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