# How do you simplify (- 5) * ( - 5) 2?

Nov 27, 2017

I'm not sure if you meant to write $\left(- 5\right) \cdot {\left(- 5\right)}^{2}$ or $\left(- 5\right) \cdot \left(- 5\right)$ times 2, so I'm going to solve both.

#### Explanation:

If you meant $\left(- 5\right) \cdot {\left(- 5\right)}^{2}$:

First, we know that ${\left(- 5\right)}^{2} = \left(- 5\right) \left(- 5\right) = 25$

$- 5 \cdot 25 = - 125$

If you meant $\left(- 5\right) \cdot 2 \left(- 5\right)$:
$- 5 \cdot - 10 = 50$

Nov 27, 2017

Presuming your question is $\left(- 5\right) {\left(- 5\right)}^{2}$
the answer is $- 125$

#### Explanation:

The problem asks you to compute the product of two quantities.
One is the amount ${\left(- 5\right)}^{2}$
According to the rules for the Order of Operations,
solve the exponents first.

The "squared" symbol applies only to the $\left(- 5\right)$ that it is touching,
so ${\left(- 5\right)}^{2}$ is solved this way:

. . . .${\left(- 5\right)}^{2}$
. . . . ╱ ╲
$\left(- 5\right) \left(- 5\right)$
. . . .╲ . ╱
. . . $+ 25$

Now the problem is
$\left(- 5\right) \left(25\right)$

That product is $- 125$ $\leftarrow$ answer

$- 125$
............................

In the unlikely event that the problem is
$\left(- 5\right) \left(- 5\right) \left(2\right)$

Solve the problem step-by-step

$\left(- 5\right) \times \left(- 5\right) \times \left(2\right)$
. . . . ╲     ╱
. . . . . . .$25$. . . . . . $\times \left(2\right)$
. . . . . . . . .╲          ╱
. . . . . . . . . . . . $50$ $\leftarrow$ answer

$50$