Exponents And Polynomials: Algebra Trivia Quiz

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.

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.

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.

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.

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.

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.

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.

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.

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.