How do I Evaluate (−9)²

Mathematics

2 answers:

Morgarella [4.7K]3 years ago

6 0

Answer:

Step-by-step explanation:

you evaluate by mutiplying the number with the exponent, which is -9 multiplied by -9, which is 81 because 2 negatives multipled or divided is a positive. hope this helped a bit

kap26 [50]3 years ago

5 0

Answer:

Step-by-step explanation:

Here, some steps to evaluate (-9)².

Step 1 :- A negative base raised to an even powers equal positive.

9 ²

Step 2 :- Write exponentiation as multiplicaton.

9 × 9

Step 3 :- Multiply it .

Another way to evaluate ( -9 ) ².

Evaluate by multiply with it's exponent.

-9 × -9

When two negative sign combine they formed positive

So, after multiplying we get 81.

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How many positive integers $n$ satisfy $127 \equiv 7 \pmod{n}$? $n=1$ is allowed.

Svetllana [295]

Naturally, any integer $n$ larger than 127 will return $127\equiv127\mod n$ , and of course $127\equiv0\mod127$ , so we restrict the possible solutions to $1\le n$ .

Now,

$127\equiv7\mod n$

is the same as saying there exists some integer $k$ such that

$127=nk+7$

We have

$\implies 120=nk$

which means that any $n$ that satisfies the modular equivalence must be a divisor of 120, of which there are 16: $\{1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120\}$ .

In the cases where the modulus is smaller than the remainder 7, we can see that the equivalence still holds. For instance,

$127=21\cdot6+1\iff127\equiv1\equiv7\mod6$

(If we're allowing $n=1$ , then I see no reason we shouldn't also allow 2, 3, 4, 5, 6.)