Simplify fourth root of d*d^24

$\sqrt[4]{d} \cdot d^{24}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{d}$ as $d^{\frac{1}{4}}$ .

$d^{\frac{1}{4}} d^{24}$

Step 2

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

$d^{\frac{1}{4} + 24}$

Step 3

To write $24$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$d^{\frac{1}{4} + 24 \cdot \frac{4}{4}}$

Step 4

Combine $24$ and $\frac{4}{4}$ .

$d^{\frac{1}{4} + \frac{24 \cdot 4}{4}}$

Step 5

Combine the numerators over the common denominator.

$d^{\frac{1 + 24 \cdot 4}{4}}$

Step 6

Simplify the numerator.

Multiply $24$ by $4$ .

$d^{\frac{1 + 96}{4}}$

Add $1$ and $96$ .

$d^{\frac{97}{4}}$