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
Tcecarenko [31]
3 years ago
6

Simplify each expression. Use positive exponents.

Mathematics
2 answers:
mario62 [17]3 years ago
4 0

Answer:

Step-by-step explanation:

(A) The given expression is:

m^3n^{-6}p^0

Simplifying this expression, we get

=m^3n^{-6}(1)

=\frac{m^3}{n^6}

which is the required simplified form.

(B) The given expression is:

\frac{a^4b^{-3}}{ab^{-2} }

Simplifying the above equation using the exponent rule, we have

=\frac{a^3}{b}

which is the required simplified form.

(C) The given expression is:

(x^{-2}y^{-4}x^3)^{-2}

Simplifying this expression, we get

=(\frac{x}{y^4})^{-2}

=(\frac{y^4}{x})^2

=\frac{y^8}{x^2}

which is the required simplified form.

Semmy [17]3 years ago
3 0
To simplify each expression, we need to group all the terms that have the same bases and flock them if necessary to one side. One rule that applies is that negative exponents goes to the other side in order to be positive.

<span>1. m3n-6p0 ; p0 =1 , so, m3/n6
2. </span><span>a^4b^-3/ab^-2  = a^4a-1 / b^-2b^3 = a^3/b
3. </span><span>(x^-2y^-4x^3) -2 = (x^-2x^3 y^-4 )^-2 = (x/y^4)^-2 = y^16/x^2</span>
You might be interested in
You put $200 in a savings account. The account earns 2% simple interest
Black_prince [1.1K]

Answer:

interest total after 5 years is $20.82

Step-by-step explanation:

6 0
2 years ago
(3a2 – 5ab + b2) + (–3a2 + 2b2 + 8ab) Which of the following shows the sum of the polynomials rewritten with like terms grouped
Mila [183]
<span>[3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2)</span><span>
</span>
6 0
3 years ago
Read 2 more answers
How to know if a function is periodic without graphing it ?
zhenek [66]
A function f(t) is periodic if there is some constant k such that f(t+k)=f(k) for all t in the domain of f(t). Then k is the "period" of f(t).

Example:

If f(x)=\sin x, then we have \sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x, and so \sin x is periodic with period 2\pi.

It gets a bit more complicated for a function like yours. We're looking for k such that

\pi\sin\left(\dfrac\pi2(t+k)\right)+1.8\cos\left(\dfrac{7\pi}5(t+k)\right)=\pi\sin\dfrac{\pi t}2+1.8\cos\dfrac{7\pi t}5

Expanding on the left, you have

\pi\sin\dfrac{\pi t}2\cos\dfrac{k\pi}2+\pi\cos\dfrac{\pi t}2\sin\dfrac{k\pi}2

and

1.8\cos\dfrac{7\pi t}5\cos\dfrac{7k\pi}5-1.8\sin\dfrac{7\pi t}5\sin\dfrac{7k\pi}5

It follows that the following must be satisfied:

\begin{cases}\cos\dfrac{k\pi}2=1\\\\\sin\dfrac{k\pi}2=0\\\\\cos\dfrac{7k\pi}5=1\\\\\sin\dfrac{7k\pi}5=0\end{cases}

The first two equations are satisfied whenever k\in\{0,\pm4,\pm8,\ldots\}, or more generally, when k=4n and n\in\mathbb Z (i.e. any multiple of 4).

The second two are satisfied whenever k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}, and more generally when k=\dfrac{10n}7 with n\in\mathbb Z (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when k is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

Let's verify:

\sin\left(\dfrac\pi2(t+20)\right)=\sin\dfrac{\pi t}2\underbrace{\cos10\pi}_1+\cos\dfrac{\pi t}2\underbrace{\sin10\pi}_0=\sin\dfrac{\pi t}2

\cos\left(\dfrac{7\pi}5(t+20)\right)=\cos\dfrac{7\pi t}5\underbrace{\cos28\pi}_1-\sin\dfrac{7\pi t}5\underbrace{\sin28\pi}_0=\cos\dfrac{7\pi t}5

More generally, it can be shown that

f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))

is periodic with period \mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n).
4 0
3 years ago
When your income is more than your expenses, you have _____.
blagie [28]
<span>When your income is more than your expenses, y</span>ou have surplus

3 0
3 years ago
Read 2 more answers
How many seconds in an 8 hour work day
aliina [53]
1 hour=3600 seconds
8 times 3600 =28800
8 0
3 years ago
Read 2 more answers
Other questions:
  • How many square inches are needed to cover a square foot
    12·2 answers
  • 26 as a fraction in simplest form
    12·1 answer
  • Can you please help me
    14·1 answer
  • Micah is buying gravel for a rock garden that will be edged by a circular metal border. She will use 110 feet of metal edging fo
    14·1 answer
  • What is the slope of the line that passes through the points (−4,−3) and (14,0)?
    12·1 answer
  • Is Water is stored in response to changing demand a cause or effect
    7·2 answers
  • A company lost $1.2 million in its first year, lost $0.9 million in the second year, and lost
    11·1 answer
  • I need help right now!!!
    12·1 answer
  • Match the expression is equivalent to 5(2x+3) when using the distributive property?
    11·1 answer
  • Unit 1.4-1.5 CFA
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!