To generate an equivalent expression, we can use the property of integer exponents that states (a^b)^c = a^(b*c).
In this case, we have (5^-3)^6 * 5^17 * 10^-2.
Using the property mentioned above, we can simplify this expression as (5^(-3*6)) * 5^17 * 10^-2.
Now, we need to simplify the exponents:
-3*6 = -18
-2 = -2
Therefore, the equivalent expression is 5^-18 * 5^17 * 10^-2.
Using the property of integer exponents that states a^b * a^c = a^(b+c), we can further simplify this expression as 5^(-18+17) * 10^-2.
-18+17 = -1, so our expression becomes 5^(-1) * 10^-2.
Finally, using the property of integer exponents that states a^-b = 1/a^b, we can write this expression as 1/5^1 * 1/10^2 or 1/5 * 1/100.
Simplifying further, we get 1/500.
Therefore, the equivalent expression is B. 1 over 500.
Apply the Properties of Integer Exponents to generate an equivalent expression to
(5−3)6⋅ 51710−2(1 point)
Responses
A. 1 over 20,
B. 1 over 500,
C. 500,
D. 20
7 answers
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alright Which of the following is not a true statement?(1 point)
7 × 10^−2 is 1,000 times as great as 7 × 10^−6
2 x 10^6 is 10 times as great as 2 x 10^5
9 x 10^-4 is 1,000 times as great as 9 x 10^-7
4 x 10^8 is 100 times as great as 4 x 10^6
7 × 10^−2 is 1,000 times as great as 7 × 10^−6
2 x 10^6 is 10 times as great as 2 x 10^5
9 x 10^-4 is 1,000 times as great as 9 x 10^-7
4 x 10^8 is 100 times as great as 4 x 10^6
Let's analyze each statement:
Statement 1: 7 × 10^-2 is 1,000 times as great as 7 × 10^-6.
To compare the magnitude of these numbers, we can divide them:
(7 × 10^-2) / (7 × 10^-6) = (10^-2) / (10^-6) = 10^(-2 - (-6)) = 10^(-2 + 6) = 10^4 = 10,000.
Since 10,000 is not equal to 1,000, this statement is false.
Statement 2: 2 x 10^6 is 10 times as great as 2 x 10^5.
To compare the magnitude of these numbers, we can divide them:
(2 x 10^6) / (2 x 10^5) = (10^6) / (10^5) = 10^(6 - 5) = 10^1 = 10.
Since 10 is equal to 10, this statement is true.
Statement 3: 9 x 10^-4 is 1,000 times as great as 9 x 10^-7.
To compare the magnitude of these numbers, we can divide them:
(9 x 10^-4) / (9 x 10^-7) = (10^-4) / (10^-7) = 10^(-4 - (-7)) = 10^(-4 + 7) = 10^3 = 1,000.
Since 1,000 is equal to 1,000, this statement is true.
Statement 4: 4 x 10^8 is 100 times as great as 4 x 10^6.
To compare the magnitude of these numbers, we can divide them:
(4 x 10^8) / (4 x 10^6) = (10^8) / (10^6) = 10^(8 - 6) = 10^2 = 100.
Since 100 is equal to 100, this statement is true.
Therefore, the statement that is not true is statement 1: 7 × 10^-2 is not 1,000 times as great as 7 × 10^-6.
The correct answer is: A. 7 × 10^−2 is 1,000 times as great as 7 × 10^−6.
Statement 1: 7 × 10^-2 is 1,000 times as great as 7 × 10^-6.
To compare the magnitude of these numbers, we can divide them:
(7 × 10^-2) / (7 × 10^-6) = (10^-2) / (10^-6) = 10^(-2 - (-6)) = 10^(-2 + 6) = 10^4 = 10,000.
Since 10,000 is not equal to 1,000, this statement is false.
Statement 2: 2 x 10^6 is 10 times as great as 2 x 10^5.
To compare the magnitude of these numbers, we can divide them:
(2 x 10^6) / (2 x 10^5) = (10^6) / (10^5) = 10^(6 - 5) = 10^1 = 10.
Since 10 is equal to 10, this statement is true.
Statement 3: 9 x 10^-4 is 1,000 times as great as 9 x 10^-7.
To compare the magnitude of these numbers, we can divide them:
(9 x 10^-4) / (9 x 10^-7) = (10^-4) / (10^-7) = 10^(-4 - (-7)) = 10^(-4 + 7) = 10^3 = 1,000.
Since 1,000 is equal to 1,000, this statement is true.
Statement 4: 4 x 10^8 is 100 times as great as 4 x 10^6.
To compare the magnitude of these numbers, we can divide them:
(4 x 10^8) / (4 x 10^6) = (10^8) / (10^6) = 10^(8 - 6) = 10^2 = 100.
Since 100 is equal to 100, this statement is true.
Therefore, the statement that is not true is statement 1: 7 × 10^-2 is not 1,000 times as great as 7 × 10^-6.
The correct answer is: A. 7 × 10^−2 is 1,000 times as great as 7 × 10^−6.
Find the cube root of -27: −27−−−−√3 (1 point)
The cube root of -27 can be written as -27^(1/3).
To solve this, we need to find a number that, when cubed, equals -27.
When we cube a positive number, the result is positive. However, when we cube a negative number, the result is negative. Therefore, the cube root of -27 is negative.
Calculating the cube root of 27:
-27^(1/3) = -3
Therefore, the cube root of -27 is -3.
The correct answer is: -3.
To solve this, we need to find a number that, when cubed, equals -27.
When we cube a positive number, the result is positive. However, when we cube a negative number, the result is negative. Therefore, the cube root of -27 is negative.
Calculating the cube root of 27:
-27^(1/3) = -3
Therefore, the cube root of -27 is -3.
The correct answer is: -3.