Algebra Examples

${(8^{3})}^{7} = 8^{n}$

Step 1

Rewrite the equation as $8^{n} = {(8^{3})}^{7}$ .

$8^{n} = {(8^{3})}^{7}$

Step 2

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

$8^{n} = 8^{3 \cdot 7}$

Step 3

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

$n = 3 \cdot 7$

Step 4

Multiply $3$ by $7$ .

$n = 21$