Evaluate 4(8^x)=64

$4 (8^{x}) = 64$

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

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

Rewrite $8$ as $2^{3}$ .

$2^{2} \cdot {(2^{3})}^{x} = 64$

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

$2^{2} \cdot 2^{3 x} = 64$

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

$2^{2 + 3 x} = 64$

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

$2^{2 + 3 x} = 2^{6}$

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

$2 + 3 x = 6$

Solve for $x$ .

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

Subtract $2$ from both sides of the equation.

$3 x = 6 - 2$

Subtract $2$ from $6$ .

$3 x = 4$

Divide each term in $3 x = 4$ by $3$ and simplify.

Divide each term in $3 x = 4$ by $3$ .

$\frac{3 x}{3} = \frac{4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{4}{3}$

Divide $x$ by $1$ .

$x = \frac{4}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{3}$

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

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