Is the sentence Forecasters predicted six more weeks of winter this year and complete sentence?
No, the sentence "Forecasters predicted six more weeks of winter this year" is not a complete sentence. It is a dependent clause because it lacks a subject or verb to make it grammatically complete.
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Which of the following correctly used the Product Rule of Exponents to simplify the expression 100 to the 8th power ⋅ 100 to the 7th power?
a. 10,000 to the 15th power
b. 200 to the 15th power
c. 100 to the 15th power
d. 100 to the 56th power
To simplify the expression 100 to the 8th power ⋅ 100 to the 7th power using the Product Rule of Exponents, we add the exponents together.
Thus, 100 to the 8th power ⋅ 100 to the 7th power can be written as 100 to the (8 + 7) power.
Therefore, the correct answer is:
d. 100 to the 15th power
Find the numerical equivalent of 10 to the 2nd power ⋅10 to the 3rd power.
To find the numerical equivalent of 10 to the 2nd power ⋅ 10 to the 3rd power, we can use the Product Rule of Exponents and add the exponents together.
10 to the 2nd power is 10 multiplied by itself twice, which equals 100.
10 to the 3rd power is 10 multiplied by itself three times, which equals 1000.
To find the numerical equivalent, we multiply these two numbers together:
100 × 1000 = 100,000.
Therefore, the numerical equivalent of 10 to the 2nd power ⋅ 10 to the 3rd power is 100,000.
Find the numerical equivalent of 2 to the 5th power ⋅ 2 to the −2 power.
To find the numerical equivalent of 2 to the 5th power ⋅ 2 to the −2 power, we can use the Product Rule of Exponents and add the exponents together.
2 to the 5th power is 2 multiplied by itself five times, which equals 32.
2 to the −2 power means we need to take the reciprocal of 2 squared. So, 2 to the −2 power is equal to 1 divided by 2 squared, which is 1/4.
To find the numerical equivalent, we multiply these two numbers together:
32 × 1/4 = 32/4 = 8.
Therefore, the numerical equivalent of 2 to the 5th power ⋅ 2 to the −2 power is 8.