Solve for t z^t*z^5=z^15

$z^{t} \cdot z^{5} = z^{15}$

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

$z^{t + 5} = z^{15}$

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

$t + 5 = 15$

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

Subtract $5$ from both sides of the equation.

$t = 15 - 5$

Subtract $5$ from $15$ .

$t = 10$