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Anvisha [2.4K]
3 years ago
9

Exponents and Powers Question Need help, please answer with explanation.

Mathematics
1 answer:
alex41 [277]3 years ago
6 0

Answer:

  a = -1

Step-by-step explanation:

The sign of a number raised to an even power is irrelevant. That means we can rewrite (-25)² as (-5)⁴. Doing so lets us combine the factors like so ...

  (-5)^{a+2}\times (-5)^4=(-5)^5\\\\(-5)^{a+2+4}=(-5)^5\\\\a+6=5 \qquad\text{equating exponents}\\\\a=-1 \qquad\text{subtract 6}

Here, we used the rule of exponents ...

  (a^b)(a^c) = a^(b+c)

_____

The business of "equating exponents" is equivalent to taking logarithms. In general, the logarithm of a number to a negative base is not defined. However, for the case of integer exponents we have here, there is no problem with doing what we did.

_____

<em>Check of the answer</em>

(-5)^1 × (-25)^2 = (-5)^5

-5 × 625 = -3125 . . . . true

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Which expression represents the sentence "five times a number, n"
olga_2 [115]

Answer:

5n

Step-by-step explanation:

it's 5 times N. So it's 5×N, but with Algebra you don't necessarily need to include the multiplication sign

5 0
2 years ago
Read 2 more answers
1. Last week, Mr. Key worked for 50 hours. This week, he work for 58 hours. 2p
quester [9]

Answer:

  16% increase

Step-by-step explanation:

A percentage change can be calculated from ...

  percentage change = ((new value)/(old value) -1) × 100%

  = (58/50 -1) × 100% = (1.16 -1) × 100%

  = 16%

Mr. Key's work hours increased 16% from last week to this.

5 0
3 years ago
Estimate. Then find the difference.<br><br> 324-285=
mafiozo [28]
            If rounding to the hundreds
To estimate round 324 and 285 to the closest hundred.
300 - 300
Then subtract 300 - 300 =
0
               If rounding to the tens
To estimate round 324 and 285 to the nearest ten.
320 - 290 
Then subtract 320 - 290 =
30
7 0
3 years ago
Read 2 more answers
Which equation can be used to find the value of a?
masya89 [10]
They can all be used. 

A. a – 42 = 91
        +42    +42
       --------------
      a= 133

B. 42 + a = 91
     -42        -42
____________
         a= 49

C. 91 + a = 42
     -91        -91
   -----------------
       a= - 49

D. a – 91 = 42
        +91    +91
     ---------------
       a= 133
6 0
3 years ago
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A man bought a bicycle for $400 and sold it at a loss of 35%. How much money did he lose?
DedPeter [7]
If he bought the bike for $400 and lost 35% of his profit, you would divide 35 by 100. Next, you would multiply that number (0.35) by 400. When you do that, you get an answer of $140. In conclusion, if he bought the bike for $400 and sold it at a loss of 35%, he would lose $140 from that $400. 

Additionally, if you wanted to know what exactly he sold it for, you would simply subtract 140 from 400. Which would be $260.

So, he bought the bike for $400, but when he resold it, he lost $140 of that pay. Basically, he resold the bike for $260. 

I hope this helps! :) Let me know if you need help with anything else!
8 0
3 years ago
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