Question

CHOSSE A NUMBER ONLY ANSWER NOWW WORTH 100POINTS
Which rules of exponents will be used to evaluate this expression? Check all that apply. StartFraction left-brace (negative 8) Superscript 4 Baseline right-brace Superscript negative 5 Baseline Over (negative 8) Superscript 6 Baseline EndFraction. 1.product of powers 2.quotient of powers 3.power of power 4.power of a product 5.negative exponent 6.zero exponent.

Answer 1

GIVEN :

The expression is $\frac{((-8)^4)^{-5}}{(-8)^6}$

TO FIND :

The rules of exponents will be used to evaluate the given expression.

SOLUTION :

Given expression is $\frac{((-8)^4)^{-5}}{(-8)^6}$

Now solving the given expression as below:

$\frac{((-8)^4)^{-5}}{(-8)^6}$

By using the Power Rule for Exponents

For any positive number x and integers a and b:

$(x^a)^b=x^{a.b}$

$=\frac{(-8)^{-20}}{(-8)^6}$

By using the Quotient Rule for Exponents

For any number  and any integers a and b:

$\frac{x^a}{x^b}=x^{a-b}$

$=(-8)^{-20-6}$

$=(-8)^{-26}$

By using the Negative Rule of Exponents

$a^{-n}=\frac{1}{a^n}$ , $a\neq 0$

$=\frac{1}{(-8)^{26}}$

$=\frac{1}{8^{26}}$ (since power is even )

∴ $\frac{((-8)^4)^{-5}}{(-8)^6}=\frac{1}{8^{26}}$

Hence the rules of exponents 2.Quotient of powers 3.Power of power 5.Negative exponent are used to evaluate the given expression.

Answer 2

Answer:

Answer in the above picture