Solve for x b^3*(b^4)^2=b^x

$b^{3} \cdot {(b^{4})}^{2} = b^{x}$

Step 1

Rewrite the equation as $b^{x} = b^{3} \cdot {(b^{4})}^{2}$ .

$b^{x} = b^{3} \cdot {(b^{4})}^{2}$

Step 2

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

$b^{x} = b^{3} \cdot b^{4 \cdot 2}$

Step 3

Multiply $b^{3}$ by $b^{4 \cdot 2}$ by adding the exponents.

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

$b^{x} = b^{3 + 4 \cdot 2}$

Multiply $4$ by $2$ .

$b^{x} = b^{3 + 8}$

Add $3$ and $8$ .

$b^{x} = b^{11}$

Step 4

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

$x = 11$