Evaluate 10/(10^(3/4))

$\frac{10}{10^{\frac{3}{4}}}$

Step 1

Move $10^{\frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$10 \cdot 10^{- \frac{3}{4}}$

Step 2

Multiply $10$ by $10^{- \frac{3}{4}}$ by adding the exponents.

Multiply $10$ by $10^{- \frac{3}{4}}$ .

Raise $10$ to the power of $1$ .

$10^{1} \cdot 10^{- \frac{3}{4}}$

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

$10^{1 - \frac{3}{4}}$

Write $1$ as a fraction with a common denominator.

$10^{\frac{4}{4} - \frac{3}{4}}$

Combine the numerators over the common denominator.

$10^{\frac{4 - 3}{4}}$

Subtract $3$ from $4$ .

$10^{\frac{1}{4}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$10^{\frac{1}{4}}$

Decimal Form:

$1.77827941 \dots$