Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for
n: ((-7)/(5))^(11)÷((-7)/(5))^(3)=((-7)/(5))^(2n+2)

Solve for $n$ : $(\frac{-7}{5})^{11}$ $÷$ $(\frac{-7}{5})^{3}$ $=$ $(\frac{-7}{5})^{2n+2}$

View step-by-step help

View step-by-step help

Multiplication with rational exponents

Full solution

Q. Solve for

n

:

(\frac{-7}{5})^{11}

÷

(\frac{-7}{5})^{3}

=

(\frac{-7}{5})^{2n+2}

Simplify Expression: Step $1$ : Simplify the expression using the properties of exponents. $\newline$ $(-\frac{7}{5})^{11} \div (-\frac{7}{5})^{3} = (-\frac{7}{5})^{11-3}$ $\newline$ = $(-\frac{7}{5})^{8}$
Set Equal and Solve: Step $2$ : Set the simplified expression equal to the given expression and solve for $n$ . $\left(\frac{-7}{5}\right)^{8} = \left(\frac{-7}{5}\right)^{2n+2}$ $8 = 2n + 2$
Final Solution: Step $3$ : Solve for $n$ . $\newline$ $8 - 2 = 2n$ $\newline$ $6 = 2n$ $\newline$ $n = \frac{6}{2}$ $\newline$ $n = 3$

More problems from Multiplication with rational exponents

Question

\newline

81^{\frac{1}{2}}

\newline

Posted 3 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 3 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

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

\newline

Posted 3 months ago

Question

Simplify. Assume all variables are positive.

\newline

(2r^{\frac{1}{3}})^8

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

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

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

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

\newline

\newline

Posted 3 months ago

Question

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

Posted 2 months ago

Question

\newline

32^{(-1/5)}

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

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

\newline

\newline

Posted 3 months ago

Question

Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

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

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

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

\newline

\newline

Posted 2 months ago