Apply All Exponent Rules Practice

Question

Math 8 Q1 (Pre-Algebra) / Exponent Rules

Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7 ⋅ 3^−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

3^7⋅3^−9=___

Answer 1

To apply the properties of integer exponents, we can use the rule that states:

a^m ⋅ a^n = a^(m+n)

Using this rule, we can rewrite the expression 3^7 ⋅ 3^−9 as:

3^(7+(-9))

Simplifying the exponent, we get:

3^(-2)

Since the exponent is negative, we can rewrite it as 1 over the positive exponent:

1/3^2

Simplifying further, we get:

1/9

Therefore, 3^7 ⋅ 3^−9 is equivalent to 1/9.

Answer 2

I have no idea how long ago this was but if you still need the answers:
Question 1: 1/9
(Use the product rule of exponents to make 3^7 x 3^-9 into 3^-2 {7 + -9 = -2} which is 1/3^2 which is also 1/9)
Question 2: 64
(Use the quotient rule of exponents to make 2^2 / 2^-4 into 2^6 {2 - -4 = 6}, which solved is 64)
Question 3: -8/25
Question 4: 1/81
(Use the Zero power rule of exponents to make the numerator 1, then solve for 3^4, which is 81)
Question 5:
7/16

Answer 3

long division is correct ty
x anonymous