The numbers in order from smallest to largest on the far left to the far right are:
|-5|, -3^2, radical symbol 9, -3, 2^3, |4|.
smallest on the far left and largest on the far right.
|4|, radical symbol 9, -3, |-5|, -3^2, and 2^3
7 answers
Simplify: 3^2×3^−1/5^−2×2^0
Adam wrote: 3^−2×5^2/2
Nick wrote: 3×5^2
Shane wrote: 3^−3/5^2
Who was correct and why?
Adam wrote: 3^−2×5^2/2
Nick wrote: 3×5^2
Shane wrote: 3^−3/5^2
Who was correct and why?
To simplify the expression 3^2 × 3^(-1) / 5^(-2) × 2^0, we can apply the rules of exponents.
First, let's simplify the individual exponential terms separately:
3^2 = 3 × 3 = 9
3^(-1) = 1 / 3^1 = 1 / 3
5^(-2) = 1 / 5^2 = 1 / 25
2^0 = 1
Now, let's substitute these simplified values back into the original expression:
9 × (1/3) / (1/25) × 1
Now, let's simplify further:
9 × (1/3) = 9/3 = 3
(1/25) × 1 = 1/25
Now, our expression simplifies to:
3 / (1/25)
To divide by a fraction, we multiply by its reciprocal:
3 × (25/1) = 3 × 25 = 75
Therefore, the correct simplification is 75.
Comparing it to the answers given by Adam, Nick, and Shane:
- Adam wrote: 3^(-2) × 5^2 / 2. This is not the same as our simplification, so Adam is incorrect.
- Nick wrote: 3 × 5^2. This is not the same as our simplification, so Nick is incorrect.
- Shane wrote: 3^(-3) / 5^2. This is not the same as our simplification, so Shane is incorrect.
None of the given answers is correct. The correct simplification is 75.
First, let's simplify the individual exponential terms separately:
3^2 = 3 × 3 = 9
3^(-1) = 1 / 3^1 = 1 / 3
5^(-2) = 1 / 5^2 = 1 / 25
2^0 = 1
Now, let's substitute these simplified values back into the original expression:
9 × (1/3) / (1/25) × 1
Now, let's simplify further:
9 × (1/3) = 9/3 = 3
(1/25) × 1 = 1/25
Now, our expression simplifies to:
3 / (1/25)
To divide by a fraction, we multiply by its reciprocal:
3 × (25/1) = 3 × 25 = 75
Therefore, the correct simplification is 75.
Comparing it to the answers given by Adam, Nick, and Shane:
- Adam wrote: 3^(-2) × 5^2 / 2. This is not the same as our simplification, so Adam is incorrect.
- Nick wrote: 3 × 5^2. This is not the same as our simplification, so Nick is incorrect.
- Shane wrote: 3^(-3) / 5^2. This is not the same as our simplification, so Shane is incorrect.
None of the given answers is correct. The correct simplification is 75.
To simplify this expression, 6x4⋅3x2 which would be the correct steps?(1 point) Responses Multiply 6 x 3 for the numbers; then add 2 + 4 for the exponent on x. Multiply 6 x 3 for the numbers; then add 2 + 4 for the exponent on x. You cannot simplify this expression because these are not like terms. You cannot simplify this expression because these are not like terms. Multiply 6 x 3 for the numbers; then multiply 2 x 4 for the exponent on x. Multiply 6 x 3 for the numbers; then multiply 2 x 4 for the exponent on x. Add 6 + 3 for the numbers; then multiply 2 x 4 to get the exponent for x.
To simplify the expression 6x4⋅3x2, the correct steps would be:
Multiply 6 x 3 for the numbers to get 18, then multiply the exponents 4 x 2 to get 8.
So the simplified expression would be 18x^8.
Multiply 6 x 3 for the numbers to get 18, then multiply the exponents 4 x 2 to get 8.
So the simplified expression would be 18x^8.
On an average weekend, 17^4 people visit Times Square and 17^6 people visit the Great Wall of China. On an average weekend, how many times more people visit the Great Wall of China than Times Square?
To find out how many times more people visit the Great Wall of China than Times Square on an average weekend, we need to compare the two numbers.
The number of people who visit Times Square is given by 17^4.
The number of people who visit the Great Wall of China is given by 17^6.
To find the difference, we divide the number of people who visit the Great Wall of China by the number of people who visit Times Square:
17^6 / 17^4 = 17^(6-4) = 17^2
Therefore, the number of people who visit the Great Wall of China on an average weekend is 17 times more than those who visit Times Square.
The number of people who visit Times Square is given by 17^4.
The number of people who visit the Great Wall of China is given by 17^6.
To find the difference, we divide the number of people who visit the Great Wall of China by the number of people who visit Times Square:
17^6 / 17^4 = 17^(6-4) = 17^2
Therefore, the number of people who visit the Great Wall of China on an average weekend is 17 times more than those who visit Times Square.
3 answers