1. Simplify ((-2x^4y^7)/(x^5))^3. Assume all variables are nonzero.

A: (-8y^21)/(x^3)

2. Simplify 3x(5y + 4) - 2xy - 10x + 6x^2

A: 13xy + 2x + 6x^2 or 6x^2 + 13xy + 2x

3. Evaluate (2.0 x 10^-7)/(8.0 x 10^-9). Write the answer in scientific notation.

A: 0.25 x 10^2

4. Evlauate f(x) = 8 - 4x for f(0), f(1/2), and f(-2).

A: 8, 6, 16

#3 is the correct value, but it is not scientific notation.

The others are ok.

1. To simplify ((-2x^4y^7)/(x^5))^3, we'll start by applying the exponent to the entire expression inside the parentheses. This means we'll raise each term to the power of 3.

(-2x^4y^7)^3 / (x^5)^3

Next, we'll simplify each term raised to the power of 3.

(-2)^3 * (x^4)^3 * (y^7)^3 / (x^5)^3

Simplifying further,

-8x^12y^21 / x^15

Now, let's apply the rule of dividing with like bases (variables). When dividing with like bases, we subtract the exponents.

-8y^21 / x^(15-12)

-8y^21 / x^3

Therefore, the simplified expression is (-8y^21) / (x^3).

2. To simplify 3x(5y + 4) - 2xy - 10x + 6x^2, we'll use the distributive property and combine like terms.

Starting with 3x(5y + 4):

3x * 5y = 15xy
3x * 4 = 12x

Now, let's combine the terms:

15xy + 12x - 2xy - 10x + 6x^2

Next, let's group the like terms:

(15xy - 2xy) + (12x - 10x) + 6x^2

Combining like terms within each group:

13xy + 2x + 6x^2

Therefore, the simplified expression is 13xy + 2x + 6x^2.

3. To evaluate (2.0 x 10^-7)/(8.0 x 10^-9), we'll divide the numerator by the denominator.

(2.0 x 10^-7) ÷ (8.0 x 10^-9)

To divide with numbers in scientific notation, we divide the coefficients (2.0 ÷ 8.0) and subtract the exponents (10^-7 ÷ 10^-9).

2.0 ÷ 8.0 = 0.25

10^-7 ÷ 10^-9 = 10^(-7 - (-9)) = 10^2

Therefore, the answer is 0.25 x 10^2 in scientific notation.

4. To evaluate f(x) = 8 - 4x for f(0), f(1/2), and f(-2), we'll substitute the given values of x into the function and evaluate.

For f(0):
f(x) = 8 - 4(0)
f(0) = 8 - 0
f(0) = 8

For f(1/2):
f(x) = 8 - 4(1/2)
f(1/2) = 8 - 2
f(1/2) = 6

For f(-2):
f(x) = 8 - 4(-2)
f(-2) = 8 + 8
f(-2) = 16

Therefore, f(0) = 8, f(1/2) = 6, and f(-2) = 16.