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

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

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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 $n$ . $\newline$ $8 - 2 = 2n$ $\newline$ $6 = 2n$ $\newline$ $n = \frac{6}{2}$ $\newline$ $n = 3$

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