Evaluate (1000/903)^(-1/15)-1

${(\frac{1000}{903})}^{- \frac{1}{15}} - 1$

Step 1

Simplify each term.

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{903}{1000})}^{\frac{1}{15}} - 1$

Apply the product rule to $\frac{903}{1000}$ .

$\frac{903^{\frac{1}{15}}}{1000^{\frac{1}{15}}} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{1000^{\frac{1}{15}}}{1000^{\frac{1}{15}}}$ .

$\frac{903^{\frac{1}{15}}}{1000^{\frac{1}{15}}} - 1 \cdot \frac{1000^{\frac{1}{15}}}{1000^{\frac{1}{15}}}$

Step 3

Combine $- 1$ and $\frac{1000^{\frac{1}{15}}}{1000^{\frac{1}{15}}}$ .

$\frac{903^{\frac{1}{15}}}{1000^{\frac{1}{15}}} + \frac{- 1000^{\frac{1}{15}}}{1000^{\frac{1}{15}}}$

Step 4

Combine the numerators over the common denominator.

$\frac{903^{\frac{1}{15}} - 1000^{\frac{1}{15}}}{1000^{\frac{1}{15}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{903^{\frac{1}{15}} - 1000^{\frac{1}{15}}}{1000^{\frac{1}{15}}}$

Decimal Form:

$- 0.00677909 \dots$