Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume all variables are positive. $\newline$ $\frac{v^{\frac{7}{6}}}{v^{\frac{13}{6}}}$ $\newline$ Write your answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ ______

View step-by-step help

View step-by-step help

Simplify expressions involving rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{v^{\frac{7}{6}}}{v^{\frac{13}{6}}}

\newline

Write your answer in the form

A

or

\frac{A}{B}

, where

A

and

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

______

Identify Expression: Identify the expression to simplify. $\newline$ We have the expression $v^{\frac{7}{6}} / v^{\frac{13}{6}}$ and we need to simplify it.
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ The quotient rule states that when we divide two expressions with the same base, we subtract the exponents: $a^m / a^n = a^{(m-n)}$ . $\newline$ So, $v^{7/6} / v^{13/6} = v^{(7/6 - 13/6)}$ .
Perform Subtraction: Perform the subtraction of the exponents. $\newline$ Subtract the exponents: $\frac{7}{6} - \frac{13}{6} = -\frac{6}{6}$ .
Simplify Result: Simplify the result. $\newline$ Since $-\frac{6}{6}$ simplifies to $-1$ , we have $v^{-1}$ .
Write Final Answer: Write the final answer with a positive exponent. $\newline$ We can rewrite $v^{-1}$ as $1/v$ because $a^{-n} = 1/a^n$ . $\newline$ So, the final answer is $1/v$ .

More problems from Simplify expressions involving rational exponents

Question

f(x)=\frac{6 x+5}{2-\sqrt{14+5 x}}

\newline

We want to find

\lim _{x \rightarrow-2} f(x)

\newline

What happens when we use direct substitution?

\newline

1

\newline

(A) The limit exists, and we found it!

\newline

(B) The limit doesn't exist (probably an asymptote).

\newline

(C) The result is indeterminate.

Posted 9 months ago

Question

x^{4}+y^{2}=17

\newline

What is the value of

\frac{d^{2} y}{d x^{2}}

(-2,1)

\newline

Give an exact number.

Posted 8 months ago

Question

What is the area of the region bound by the graphs of

f(x)=\sqrt{x-2}, g(x)=14-x

x=2

\newline

1

\newline

\frac{19}{6}

\newline

\frac{99}{2}

\newline

\frac{151}{2}

\newline

\frac{45}{2}

Posted 7 months ago

Question

g(x)=x^{\frac{4}{3}}

\newline

g^{\prime}(27)=

Posted 8 months ago

Question

\ln \left(\frac{1}{\sqrt{e}}\right)

\newline

Posted 9 months ago

Question

\ln \left(\frac{1}{e}\right)

\newline

Posted 9 months ago

Question

y=(\sin^{-1}(5x^{2}))^{3}

Posted 8 months ago

Question

\left(10x^{3}-5x^{2}-6x\right)\div\left(2x^{2}\right)

Posted 8 months ago

Question

y=\cos^{4}x\sin^{4}x

Posted 8 months ago

Question

\frac{3}{5}-\frac{3}{10}

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant