Solve for z x^5(x^3)^4=x^z

$x^{5} {(x^{3})}^{4} = x^{z}$

Step 1

Rewrite the equation as $x^{z} = x^{5} {(x^{3})}^{4}$ .

$x^{z} = x^{5} {(x^{3})}^{4}$

Step 2

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

$x^{z} = x^{5} x^{3 \cdot 4}$

Step 3

Multiply $x^{5}$ by $x^{3 \cdot 4}$ by adding the exponents.

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

$x^{z} = x^{5 + 3 \cdot 4}$

Multiply $3$ by $4$ .

$x^{z} = x^{5 + 12}$

Add $5$ and $12$ .

$x^{z} = x^{17}$

Step 4

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

$z = 17$