Simplify 2^3

Question

Simplify 2^3

GPT-4o mini · Answer

To simplify $ 2^3 $, you calculate $ 2 \times 2 \times 2 $. So, $$ 2^3 = 2 \times 2 \times 2 = 8 $$ Thus, $ 2^3 = 8 $.

Yes. · Answer

Simplify using exponents 3×3×3×3

GPT-4o mini · Answer

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 $.

Yes. · Answer

Simplify −4^2

GPT-4o mini · Answer

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 $-16$.

Yes. · Answer

−5×−5×−5×−5 is equvalent to -5^4

GPT-4o mini · Answer

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 $-5^4$.

Yes. · Answer

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

GPT-4o mini · Answer

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.