2: Y^5 x y^14=
A: 2y^19
B: y^60
C: y^19
D: 2y^60
3: w^12 ÷ w^18
A: w^30
B: w^-30
C: w^6
D: w^-6
4: Using the numbers 3, 2, and 4, which of these problems would have a solution of 4?
A: 4 x 2^3 ÷ 2^3
B: 2 x 2^3 ÷ 2^4
C: 3 x 2^3 ÷ 2^4
D: 3 x 2^4 ÷ 2^4
5: Taylor completed the problem below. Describe and correct the error in the problem.
2^-4 = -2 x -2 x -2 x -2 =16
A: Taylor changed the negative exponent to a negative base. *****
B: Taylor did not multiply correctly. The answer should be 16.
C: Taylor made the answer positive. It should be -16.
D: Taylor did not multiply by -1. The problem should be 2^-4 = (-1) 1 ÷ 2^4 = (-1) 1 ÷ 2 • 2 • 2 • 2 = 1/16
I only know the answer to the first and last question (1 and 5) someone please help with the rest.. thank you :)
2. Add the exponents, y stays as is.
3. Subtract the exponents, w stays as is, but your answer will be in a fraction.
4. Try out each answer choice, and see what makes sense and is correct.
5. Check again.
Sure, let's go through each question step by step:
2: To simplify the expression Y^5 x y^14, we can use the rule of exponents which states that when multiplying two numbers with the same base, we add the exponents. In this case, both Y^5 and y^14 have the same base (Y and y respectively). Therefore, we add the exponents: 5 + 14 = 19.
So the answer is A: 2y^19.
3: To simplify w^12 ÷ w^18, we can use the rule of exponents which states that when dividing two numbers with the same base, we subtract the exponents. In this case, both w^12 and w^18 have the same base (w). Therefore, we subtract the exponents: 12 - 18 = -6.
But since the question asks for the answer in exponent form, we write it as w^-6.
So the answer is D: w^-6.
4: We are looking for a problem using the numbers 3, 2, and 4 that has a solution of 4.
Let's go through each option:
A: 4 x 2^3 ÷ 2^3. In this case, the 2^3 in the numerator and denominator cancel out, leaving us with 4. This is the correct answer.
B: 2 x 2^3 ÷ 2^4. In this case, the 2^3 in the numerator and the 2^4 in the denominator cancel out, leaving us with 2. This is not the correct answer.
C: 3 x 2^3 ÷ 2^4. In this case, both the 2^3 and 2^4 cancel out, leaving us with 3. This is not the correct answer.
D: 3 x 2^4 ÷ 2^4. In this case, the 2^4 in the numerator and denominator cancel out, leaving us with 3. This is not the correct answer.
Therefore, the correct answer is A: 4 x 2^3 ÷ 2^3.
5: In the given problem, 2^-4 = -2 x -2 x -2 x -2 =16, we can see that Taylor made an error.
The correct calculation should be 2^-4 = (1/2^4) = 1/(2 • 2 • 2 • 2) = 1/16. Taylor incorrectly changed the sign from negative to positive and did not perform the division correctly.
Therefore, the error in the problem is described as A: Taylor changed the negative exponent to a negative base.
I hope this helps!