Question

Determine the value of the variable in each expression. What is the value of m in the quotient of powers StartFraction 9 Superscript negative 3 Over 9 squared EndFraction = StartFraction 1 Over 9 Superscript m EndFraction? options: -5 -1 1 5 What is the value of n in the quotient of powers StartFraction x Superscript negative 4 Over x Superscript negative 6 EndFraction = x Superscript n options: -10 -2 2 10 What is the value of c in the quotient of powers StartFraction (negative 11) Superscript 7 Over (Negative 11) Superscript 0 EndFraction = (Negative 11) Superscript c options: -7 0 -6 7

Answer 1

Given:

$\dfrac{9^{-3}}{9^2}=\left(\dfrac{1}{9}\right)^m$

$\dfrac{x^{-4}}{x^{-6}}=x^n$

$\dfrac{(-11)^7}{(-11)^0}=(-11)^c$

To find:

The value of m, n and c.

Solution:

$\dfrac{9^{-3}}{9^2}=\left(\dfrac{1}{9}\right)^m$

$\dfrac{1}{9^39^2}=\left(\dfrac{1}{9}\right)^m$

$\dfrac{1}{9^{3+2}}=\left(\dfrac{1}{9}\right)^m$

$\dfrac{1}{9^{5}}=\left(\dfrac{1}{9}\right)^m$

$\left(\dfrac{1}{9}\right)^5=\left(\dfrac{1}{9}\right)^m$

On comparing both sides, we get

$m=5$

Therefore, the correct option is D.

$\dfrac{x^{-4}}{x^{-6}}=x^n$

$x^{-4-(-6)=x^n$

$x^{-4+6}=x^n$

$x^{2}=x^n$

On comparing both sides, we get

$n=2$

Therefore, the correct option is C.

$\dfrac{(-11)^7}{(-11)^0}=(-11)^c$

$\dfrac{(-11)^7}{1}=(-11)^c$

$(-11)^7=(-11)^c$

On comparing both sides, we get

$c=7$

Therefore, the correct option is D.

Answer 2

Answer:

m=5

n=2

c=7

Step-by-step explanation: