Question

Simplify 2^3

Answer 1

Simplify using exponents 3×3×3×3

Answer 2

Simplify −4^2

Answer 3

−5×−5×−5×−5 is equvalent to -5^4

Answer 4

−1×−1×−1×−1×−1×−1−1×−1×−1×−1x−1×−1 is equivalent to (−1)6(−1)6 true or false

Answer 5

To simplify \( 2^3 \), you calculate \( 2 \times 2 \times 2 \).

So,

\[
2^3 = 2 \times 2 \times 2 = 8
\]

Thus, \( 2^3 = 8 \).

Answer 6

The expression \( 3 \times 3 \times 3 \times 3 \) can be simplified using exponents. Since there are four 3's being multiplied together, you can express this as:

\[
3 \times 3 \times 3 \times 3 = 3^4
\]

So, the simplified form using exponents is \( 3^4 \).

Answer 7

To simplify \(-4^2\), you need to be careful with the placement of the negative sign and the exponent.

According to the order of operations, the exponent is applied first. So, calculate \(4^2\) first:

\[
4^2 = 16
\]

Then, apply the negative sign:

\[
-4^2 = -16
\]

Therefore, the simplified result is \(-16\).

If you meant \((-4)^2\), that would be a different calculation:

\[
(-4)^2 = (-4) \times (-4) = 16
\]

But as written, \(-4^2\) simplifies to \(-16\).

Answer 8

The expression \(-5 \times -5 \times -5 \times -5\) can be simplified as follows:

When you multiply an even number of negative numbers, the result is positive. Here, we have four negative fives:

\[
(-5) \times (-5) \times (-5) \times (-5) = [(-5) \times (-5)] \times [(-5) \times (-5)] = 25 \times 25 = 625
\]

This can also be expressed using exponents. Since there are four instances of \(-5\), you can write it as:

\[
(-5)^4
\]

However, the expression \(-5^4\) is not equivalent to \(-5 \times -5 \times -5 \times -5\). Instead, \(-5^4\) is calculated as:

\[
- (5^4) = - (625) = -625
\]

So, in summary:

- \(-5 \times -5 \times -5 \times -5 = (-5)^4 = 625\)
- \(-5^4 = -625\)

Thus, \(-5 \times -5 \times -5 \times -5\) is equivalent to \((-5)^4\), not \(-5^4\).

Answer 9

Let's break down the expression you've provided:

The expression \(-1 \times -1 \times -1 \times -1 \times -1 \times -1\) consists of six instances of \(-1\) multiplied together.

Since multiplying two negative numbers gives a positive result:

- \((-1) \times (-1) = 1\)
- \((-1) \times (-1) \times (-1) \times (-1) \times (-1) \times (-1) = 1 \times 1 \times (-1) = -1\)

Therefore, the entire product of six \(-1\) values is:

\[
(-1)^6 = 1
\]

Now, for the additional expression provided, which is \(-1 \times -1 \times -1 \times -1 \times -1 \times -1\):

- The total expression simplifies to \((-1)^6\) as well.

Thus, we have two identical expressions:

\[
(-1 \times -1 \times -1 \times -1 \times -1 \times -1) = (-1)^6
\]

And also:

The statement suggests:

\[
(-1)^6(\text{-}1)^6 \text{ is equivalent to } (-1)^6 \times (-1)^6
\]

This statement is **true** because both sides evaluate to \(1 \times 1 = 1\).

So, the original statement is indeed **true**.