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.