Simplify 12^(1/8)*12^(5/6)

$12^{\frac{1}{8}} \cdot 12^{\frac{5}{6}}$

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

$12^{\frac{1}{8} + \frac{5}{6}}$

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$12^{\frac{1}{8} \cdot \frac{3}{3} + \frac{5}{6}}$

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$12^{\frac{1}{8} \cdot \frac{3}{3} + \frac{5}{6} \cdot \frac{4}{4}}$

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{8}$ by $\frac{3}{3}$ .

$12^{\frac{3}{8 \cdot 3} + \frac{5}{6} \cdot \frac{4}{4}}$

Multiply $8$ by $3$ .

$12^{\frac{3}{24} + \frac{5}{6} \cdot \frac{4}{4}}$

Multiply $\frac{5}{6}$ by $\frac{4}{4}$ .

$12^{\frac{3}{24} + \frac{5 \cdot 4}{6 \cdot 4}}$

Multiply $6$ by $4$ .

$12^{\frac{3}{24} + \frac{5 \cdot 4}{24}}$

Combine the numerators over the common denominator.

$12^{\frac{3 + 5 \cdot 4}{24}}$

Simplify the numerator.

Multiply $5$ by $4$ .

$12^{\frac{3 + 20}{24}}$

Add $3$ and $20$ .

$12^{\frac{23}{24}}$

The result can be shown in multiple forms.

Exact Form:

$12^{\frac{23}{24}}$

Decimal Form:

$10.81970352 \dots$