Exponent Rules Unit Test
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Question
Use the Product Rule of Exponents to simplify 510⋅55
To simplify 510⋅55 using the Product Rule of Exponents, we can add the exponents of the same base number, 5.
Following the Product Rule, we get:
510⋅55 = (5^10)⋅(5^5)
= 5^(10+5)
= 5^15
So, 510⋅55 simplifies to 5^15.
What is the missing exponent in the following equation?
h450h? = h215 (1 point)
To find the missing exponent in the equation h450h? = h215, we can use the Quotient Rule of Exponents. According to the Quotient Rule, when dividing two numbers with the same base, we subtract the exponents.
In this case, we have:
h450h? = h215
The base is 'h'. Since the exponents are missing, let's call them 'x' and 'y'.
Using the Quotient Rule, we can write the equation as:
h^(450-x) = h^215
To solve for the missing exponent 'y', we need to set the exponents on both sides of the equation equal to each other.
450 - x = 215
Now, we can solve for 'x':
450 - x = 215
Subtracting 450 from both sides, we get:
-x = -235
Dividing both sides by -1 (or multiplying by -1), we find:
x = 235
Therefore, the missing exponent in the equation h450h? = h215 is 235.
Simplify 1287÷1225 .
To simplify 1287 ÷ 1225, you can simply divide the numerator (1287) by the denominator (1225).
1287 ÷ 1225 = 1.05
Therefore, 1287 ÷ 1225 simplifies to 1.05.
What is the value of 6.9−20 ?(1 point)
Responses
6.9
6.9
5.9
5.9
7.9
7.9
4.9
To calculate the value of 6.9 - 20, you subtract 20 from 6.9:
6.9 - 20 = -13.1
Therefore, the value of 6.9 - 20 is -13.1.
What is the value of 6.9−2^0 ?(1 point)
Responses
6.9
6.9
5.9
5.9
7.9
7.9
4.9
To find the value of 6.9 - 2^0, we need to evaluate the exponent expression first.
2^0 is equal to 1, since any number raised to the power of 0 is equal to 1.
Therefore, the expression simplifies to:
6.9 - 1 = 5.9
Thus, the value of 6.9 - 2^0 is 5.9.
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)0+32(8−270).(2 points)
9⋅(−33)0+32(8−270) =
⋅
+32(
–
)