1.
Simplify
Correct Answer
D. X^12
Explanation
To simplify the given expression, we can combine the exponents of x. When we multiply x^32 with x^4, we add the exponents, which gives us x^(32+4) = x^36. Similarly, when we multiply x^(-4) with x^12, we add the exponents, which gives us x^(-4+12) = x^8. Finally, when we multiply x^36 with x^8, we add the exponents, which gives us x^(36+8) = x^44. However, since the answer provided is x^12, it seems like there might be a mistake or missing information in the question.
2.
Simplify
Correct Answer
B. 32a^2b^6
Explanation
The given expression is 32ab^5. In order to simplify this expression, we can combine the coefficients and the variables. The coefficient is 32, and the variables are a and b. Since there is no other expression to combine with, the coefficient and variables remain the same. Therefore, the simplified expression is 32ab^5.
3.
Simplify
Correct Answer
A. 4x^3/y
Explanation
The given expression is 4x^3/y. To simplify this expression, we can divide the numerator and denominator by 4. This gives us x^3/y, which is the same as x^3y/4. Therefore, the correct answer is 4x^3/y.
4.
Simplify
Correct Answer
C. 9x^6y^2
Explanation
The given expression is -9x^6y^3. To simplify this expression, we can divide both the coefficients (-9) and the variables (x and y) by their common factors. Since the variables have exponents, we can subtract the exponents when dividing. Therefore, the simplified expression is 9x^6y^2.
5.
Write in scientific notation: 0.000742
Correct Answer
A. 7.42 x 10^-4
Explanation
The correct answer is 7.42 x 10^-4. This is because when we write a number in scientific notation, we express it as a decimal number between 1 and 10, multiplied by a power of 10. In this case, the decimal number is 7.42, and the power of 10 is -4. This means that we move the decimal point 4 places to the left to get the original number, which is 0.000742.
6.
Neptune is miles from the sun. Write this decimal in decimal notation.
Correct Answer
B. 2,793,000,000
7.
Simplify .
Correct Answer
D. -6x^3 - 4x^2 + 3
Explanation
The given expression is a polynomial. To simplify it, we need to combine like terms. In this case, we have terms with the same variable and exponent.
Starting with the x^3 terms, we have -10x^3 and -6x^3. When we combine these, we get -16x^3.
Moving on to the x^2 terms, we have -4x^2 and -4x^2. Combining these, we get -8x^2.
Finally, we have the constant terms -3 and 3. These cancel each other out.
Putting it all together, we get -16x^3 - 8x^2. Therefore, the correct simplified form is -16x^3 - 8x^2.
8.
Simplify
Correct Answer
A. 9x^3 - 5x^2 + x - 16
Explanation
The given expression is 9x^3 - 5x^2 + x - 16. This expression cannot be simplified further since it is already in its simplest form.
9.
Simplify
Correct Answer
C. 6x^2 + x - 2
Explanation
The given expression is a fraction with a numerator of 6x^2 + 7x - 2 and a denominator of 5x^2 - x - 3. To simplify this expression, we need to factor both the numerator and the denominator. The numerator can be factored as (3x - 1)(2x + 2), and the denominator can be factored as (5x + 3)(x - 1). By canceling out the common factors of (3x - 1) and (x - 1), we are left with the simplified expression of (2x + 2)/(5x + 3). However, this does not match any of the given answer choices, so the correct answer is not provided.
10.
Simplify
Correct Answer
B. 9x^2 - 12x + 4
Explanation
The given expression is a quadratic expression in the form of 9x^2 - 12x + 4. To simplify the expression, we can combine like terms. Since there are no like terms in the given expression, we cannot further simplify it. Therefore, the correct answer is 9x^2 - 12x + 4.