Question

Apply the properties of integer exponents to generate equivalent expressions to 3⁷ • 3^-⁹ with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

3⁷ • 3^-⁹=

Answer 1

Apply the properties of integer exponents to generate equivalent expressions to 2²/2^-⁴ with only positive exponents, then solve the expression. Provide the solution as a whole number.

Answer 2

Apply the properties of integer exponents to generate equivalent expressions to 4⁰ • 5^-²/(-2)^-³ with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Answer 3

To generate equivalent expressions with only positive exponents, we can use the properties of integer exponents.

First, let's apply the property that states a^m • a^n = a^(m+n):

3^7 • 3^(-9) = 3^(7 + (-9))

Next, simplify the exponent:

3^(-2)

We can apply another property that states a^(-n) = 1/a^n:

1/3^2

Simplifying further, we have:

1/9

Therefore, the expression 3⁷ • 3^-⁹ is equal to 1/9.

Answer 4

To generate equivalent expressions with only positive exponents, we can use the properties of integer exponents.

Let's first apply the property that states a^m / a^n = a^(m-n):

2^2 / 2^(-4) = 2^(2 - (-4)) = 2^(2 + 4) = 2^6

Therefore, the expression 2²/2^-⁴ is equivalent to 2^6.

To solve this expression as a whole number, we calculate 2^6:

2^6 = 2 × 2 × 2 × 2 × 2 × 2 = 64

Therefore, the solution to the expression 2²/2^-⁴ is 64.

Answer 5

To generate equivalent expressions with only positive exponents, we can use the properties of integer exponents.

First, let's simplify each term separately.

4^0 = 1 (Any number raised to the power of 0 is equal to 1.)

5^(-2) = 1/5^2 = 1/25

(-2)^(-3) = 1/(-2)^3 = 1/(-2 × -2 × -2) = 1/(-8) = -1/8

Now let's substitute the simplified terms back into the expression:

4^0 • 5^-2 / (-2)^-3 = 1 • 1/25 / -1/8

Next, let's simplify the expression:

1 • 1/25 / -1/8 = 1/25 ÷ -1/8

To divide fractions, we can multiply by the reciprocal of the second fraction:

1/25 ÷ -1/8 = 1/25 × -8/1

Multiplying the numerators and denominators:

1/25 × -8/1 = -8/25

Therefore, the solution to the expression 4⁰ • 5^-² / (-2)^-³ is -8/25.