All categories

3 years ago

Rewrite the expression with a rational exponent as a radical expression.

Mathematics

1 answer:

Vilka [71]3 years ago

5 0

Answer:

$\sqrt{5}$

Step-by-step explanation:

we know that

The "power rule" tells us that to raise a power to a power, just multiply the exponents

$(a^{m})^{n}=a^{m*n}$

we have

$(5^{\frac{3}{4}})^{\frac{2}{3}}$

Applying the "power rule"

$(5^{\frac{3}{4}})^{\frac{2}{3}}=5^{\frac{3}{4}*\frac{2}{3}}=5^{\frac{1}{2}}=\sqrt{5}$

You might be interested in

Rewrite in simplest radical form 1 . show each step of your process.

morpeh [17]

Answer:

what is this russian math?

Step-by-step explanation:

4 0

3 years ago

Suppose that the position of one particle at time is given by x1=3sin t, y1 = 2 cos t, 0 ≤ t ≤ 2π and the position of a second p

Mashcka [7]

Answer:

there is no collision between the particles

Step-by-step explanation:

for the first particle

x1=3sin t, y1 = 2 cos t, 0 ≤ t ≤ 2π

for the second particle

x2 = -3 + cos t, y2 = 1 + sin t, 0 ≤ t ≤ 2π

then for the collision

x1=x2 → 3*sin t = -3 + cos t → sin t= -1 + (cos t)/3→ 1+ sin t = (1/3)cos t

y1=y2 → 1 + sin t = 2 cos t → (1/3)cos t = 2 cos t →(1/3) = 2

since 1/3 ≠ 2 there is no collision between the particles

6 0

3 years ago

a 36 inch board is to be cut into three pieces so that the piece is twice as long as the first piece and the third piece is 3 ti

ICE Princess25 [194]

Answer:

First piece = 6 inches

Second piece = 12 inches

Third piece = 18 inches

Step-by-step explanation:

Length of the first piece = x

Length of the second piece = 2x

Length of the third piece = 3x

Total length is 36 inches:

x + 2x + 3x = 36

6x = 36

x = 6

Therefore, the lengths are:

First piece = 6 inches

Second piece = 12 inches

Third piece = 18 inches

7 0

3 years ago

Suppose Kaitlin places $6500 in an account that pays 12% interest compounded each year.

Leya [2.2K]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for 1 year}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6500\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1 \end{cases}$

$\bf A=6500\left(1+\frac{0.12}{1}\right)^{1\cdot 1}\implies A=6500(1.12)\implies A=7280 \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for 2 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6500\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}$

$\bf A=6500\left(1+\frac{0.12}{1}\right)^{1\cdot 2}\implies A=6500(1.12)^2\implies A=8153.6$

6 0

3 years ago

Is 81/4 considered a rational number

maks197457 [2]

Answer:

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator q. Numbers that are not rational are called irrational numbers. The real line consists of the union of the rational and irrational numbers. The set of rational numbers is of measure zero on the real line, so it is "small" compared to the irrationals and the continuum.

The set of all rational numbers is referred to as the "rationals," and forms a field that is denoted Q. Here, the symbol Q derives from the German word Quotient, which can be translated as "ratio," and first appeared in Bourbaki's Algèbre (reprinted as Bourbaki 1998, p. 671).

Any rational number is trivially also an algebraic number.

Examples of rational numbers include -7, 0, 1, 1/2, 22/7, 12345/67, and so on. Farey sequences provide a way of systematically enumerating all rational numbers.

The set of rational numbers is denoted Rationals in the Wolfram Language, and a number x can be tested to see if it is rational using the command Element[x, Rationals].

The elementary algebraic operations for combining rational numbers are exactly the same as for combining fractions.

It is always possible to find another rational number between any two members of the set of rationals. Therefore, rather counterintuitively, the rational numbers are a continuous set, but at the same time countable.

8 0

3 years ago