Evaluate Evaluate -7*(-7)^-4

Evaluate $- 7 \cdot {(- 7)}^{- 4}$

Step 1

Multiply $- 7$ by ${(- 7)}^{- 4}$ by adding the exponents.

Multiply $- 7$ by ${(- 7)}^{- 4}$ .

Raise $- 7$ to the power of $1$ .

${(- 7)}^{1} \cdot {(- 7)}^{- 4}$

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

${(- 7)}^{1 - 4}$

Subtract $4$ from $1$ .

${(- 7)}^{- 3}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(- 7)}^{3}}$

Step 3

Raise $- 7$ to the power of $3$ .

$\frac{1}{- 343}$

Step 4

Move the negative in front of the fraction.

$- \frac{1}{343}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{343}$

Decimal Form:

$- 0.00291545 \dots$