The expression 6-2/6^0 is equivalent to 6-2/1. Since any number divided by 1 is equal to itself, this expression simplifies to 6-2, which is equal to 4.
Therefore, the answer is not listed in the given options.
5. Which expression is equivalent to
6
−2
6
0
?
A. 1
36
B. 36
C. −
1
12
11 answers
6. Simplify the expression 4
6
• 4
−8
.
L. 16
M. 1
4
48
N. 1
16
6
• 4
−8
.
L. 16
M. 1
4
48
N. 1
16
To simplify the expression (4/6) • (4/-8), we can simplify the fractions first:
4/6 can be simplified by dividing both the numerator and denominator by 2: 2/3.
4/-8 can be simplified by dividing both the numerator and denominator by 4: 1/-2, which is equivalent to -1/2.
Now, we can multiply the simplified fractions:
(2/3) • (-1/2) = (2 • -1)/(3 • 2) = -2/6.
The fraction -2/6 can be further simplified by dividing both the numerator and denominator by 2:
-2/6 = -1/3.
Therefore, the simplified expression is -1/3, which is not listed among the given options.
4/6 can be simplified by dividing both the numerator and denominator by 2: 2/3.
4/-8 can be simplified by dividing both the numerator and denominator by 4: 1/-2, which is equivalent to -1/2.
Now, we can multiply the simplified fractions:
(2/3) • (-1/2) = (2 • -1)/(3 • 2) = -2/6.
The fraction -2/6 can be further simplified by dividing both the numerator and denominator by 2:
-2/6 = -1/3.
Therefore, the simplified expression is -1/3, which is not listed among the given options.
7. Simplify the expression 3
2
3−1
.
G. 27
H. 1
9
I. 3
2
3−1
.
G. 27
H. 1
9
I. 3
To simplify the expression (3^2/3^1), we can use the rule of exponents that states when we have the same base raised to different exponents, we can subtract the exponents:
3^2/3^1 = 3^(2-1) = 3^1 = 3.
Therefore, the simplified expression is 3, and the answer is option I.
3^2/3^1 = 3^(2-1) = 3^1 = 3.
Therefore, the simplified expression is 3, and the answer is option I.
Which expression is equivalent to
(122
)
6
.
A. 1212
B. 128
C. 246
(122
)
6
.
A. 1212
B. 128
C. 246
To find the expression that is equivalent to (122)^(1/6), we need to find the 6th root of 122.
Raising a number to the power of (1/6) is the same as finding the 6th root of the number.
Since 2^6 = 64 and 3^6 = 729, we know that the 6th root of 122 lies between 2 and 3.
We can estimate that the 6th root of 122 is approximately 2.5.
Therefore, none of the given options, A, B, or C, are equivalent to (122)^(1/6).
Raising a number to the power of (1/6) is the same as finding the 6th root of the number.
Since 2^6 = 64 and 3^6 = 729, we know that the 6th root of 122 lies between 2 and 3.
We can estimate that the 6th root of 122 is approximately 2.5.
Therefore, none of the given options, A, B, or C, are equivalent to (122)^(1/6).
Write the number 290,000,000 in
scientific notation.
R. 2.9 x 108
S. 29 x 107
T. 2.9 x 10−8
scientific notation.
R. 2.9 x 108
S. 29 x 107
T. 2.9 x 10−8
W. 2.9 x 108 is the correct scientific notation for the number 290,000,000.
Explain: To write numbers in scientific
notation you must
notation you must
To write numbers in scientific notation, you must express the number as a product of a coefficient and a power of 10.
The coefficient must be a number between 1 and 10 (inclusive), and the power of 10 represents the number of times the decimal point is moved to the right or left to bring the number to its original magnitude.
If the original number is very large, the power of 10 will be positive. For example, 290,000,000 can be written as 2.9 x 10^8. Here, the coefficient is 2.9, and the power of 10 is 8, indicating that we move the decimal point eight places to the right.
If the original number is very small, the power of 10 will be negative. For example, 0.000029 can be written as 2.9 x 10^-5. Here, the coefficient is 2.9, and the power of 10 is -5, indicating that we move the decimal point five places to the left.
Using scientific notation helps to express very large or very small numbers in a more concise and standardized form.
The coefficient must be a number between 1 and 10 (inclusive), and the power of 10 represents the number of times the decimal point is moved to the right or left to bring the number to its original magnitude.
If the original number is very large, the power of 10 will be positive. For example, 290,000,000 can be written as 2.9 x 10^8. Here, the coefficient is 2.9, and the power of 10 is 8, indicating that we move the decimal point eight places to the right.
If the original number is very small, the power of 10 will be negative. For example, 0.000029 can be written as 2.9 x 10^-5. Here, the coefficient is 2.9, and the power of 10 is -5, indicating that we move the decimal point five places to the left.
Using scientific notation helps to express very large or very small numbers in a more concise and standardized form.
4 answers