1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
What represents the inverse of the function f(x)=4x
Yuki888 [10]

Answer:

\frac{x}{4}

Step-by-step explanation:

The given function is

f(x) = 4x

As we know

f(x) = y, which implies x= f^{-1} (y)

Therefore,

y = 4x

x = \frac{y}{4}

as x= f^{-1} (y)

So,

f^{-1} (y) = \frac{y}{4}

replacing y by x in the above expression

f^{-1} (x) = \frac{x}{4}

So our inverse function is  \frac{x}{4}

4 0
3 years ago
If the perimeter of an isosceles trapezoid is 79.53 meters, and the bases measure 25.62 meters and 33.51 meters, find the length
elixir [45]
An isosceles trapezoid is one that has 2 bases of different lengths and the other 2 sides having the same length as each other (definition of isosceles trapezoid). So if the perimeter is 79.53, the the formula is 79.53=x+x+25.62+33.51 and 79.53=2x+59.13. Solve that for x to get that x=10.2. That's your answer! Each leg is 10.2 meters long.
3 0
3 years ago
Given the equation y= -3x + 2.5 . When x is 8.5 , what value of y makes the equation true?
Len [333]

Answer: 23

Step-by-step explanation: -3(8.5)=25.5. 25.5+2.5=23

8 0
3 years ago
Please help quick!! What is the surface area of the prism?
svlad2 [7]

Lateral Surface Area. The general formula for the total surface area of a right prism is T . S . A . = p h + 2 B where represents the perimeter of the base, the height of the prism and the area of the base.

5 0
3 years ago
Read 2 more answers
At dinner, the number of quarts of water the restaurant sells is 36 fewer than twice as many as it sells at lunch. The restauran
Natasha2012 [34]
Let x be the number of quarts of water it sells at lunch

Dinner = 2x - 36

Lunch = 2x

2x + 2x - 36 = 4x - 36

4x - 36 = 144

144 - 36 = 4x

4x = 108

x = 108 divided by 4 = 27

2x = 27 x 2 = 54

The restaurant sells 54 quarts of water at lunch.
5 0
3 years ago
Read 2 more answers
Other questions:
  • If TGS = KEL, which angle in KEL corresponds to T?
    5·2 answers
  • A rectangles width is one fifth it's length and it's perimeter is 168m. Find the dimensions of the rectangle
    10·1 answer
  • What is the solution to the equation to 0.5x+3.5=6
    10·1 answer
  • One third of a number and 5 is 20
    8·1 answer
  • If cos=20/29 and it is in the 4th quadrant, what is tan2x?
    14·1 answer
  • A researcher was interested in comparing the resting heart rate of people who exercise regularly and people who do not exercise
    5·1 answer
  • How many hours and minutes elapsed from 8:00 a.m to 2:30 p.m?
    5·1 answer
  • Jack held a balloon 12 feet off the ground, straight above his head. NIGEL is standing 18 feet directly to the right of Jack.
    15·2 answers
  • Simplify: -5(3c-9) – 9c – 7c2 +5<br> What’s the answer?
    14·1 answer
  • The estimated product of 20.7 and 9.18, after rounding both factors to the nearest whole number,
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!