1.
Simplify.
14 ^ -4
A. 1 / 14 ^ 4
B. -56 ** ?
C. 1 / 14
D. 1 / 14 ^ -4
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2.
Multiply, write in scientific notation.
(9 x 10^4)(8 x 10^6)
A. 7.2 x 10^25
B. 1.7 x 10^11
C. 7.2 x 10^11 ** ?
D. 1.7 x 10^25
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3.
Write expression using single exponent.
6^a x 6^v
A. 6^a+v
B. 6^av
C. 36^av** ??
D. 36^a+v
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4.
Write expression using single exponent.
7^5 x 7^6
A. 49^30 **?
B. 7^30
C. 49^11
D. 7^11
14^-4 = 1/14^4
think about it. 14^0 = 1
1/14^4 = 14^0/14^4 = 14^(0-4) = 14^-4
on the other hand, 14*(-4) = -56
#2 ok
#3 6^a x 6^v = 6^(a+v)
review the rules of exponents
#4 same as #3
7^5 x 7^6 = 7^(5+6) = 7^11
49^30 = 49^(5*6) = (49^5)^6
Thank you!!
1. To simplify 14 ^ -4, we can rewrite it as 1 / 14 ^ 4. So, the correct answer is A. 1 / 14 ^ 4.
2. To multiply (9 x 10^4)(8 x 10^6), we can first multiply the numbers and then add the exponents of 10.
(9 x 10^4)(8 x 10^6) = 72 x 10^(4+6) = 72 x 10^10
So, the answer is C. 7.2 x 10^11.
3. When we multiply 6^a and 6^v, we add the exponents since the base is the same. Therefore, the expression can be simplified to 6^(a+v).
So, the correct answer is A. 6^(a+v).
4. When we multiply 7^5 and 7^6, we add the exponents since the base is the same. Therefore, the expression can be simplified to 7^(5+6) = 7^11.
So, the correct answer is D. 7^11.
1. To simplify 14^(-4), we need to rewrite it in a different form. The exponent -4 indicates that we need to take the reciprocal of the base raised to the positive exponent. Therefore, 14^(-4) can be simplified as 1 / 14^4.
Answer: A. 1 / 14^4
2. To multiply (9 x 10^4)(8 x 10^6), we need to multiply the coefficients and add the exponents of the powers of 10.
9 x 10^4 multiplied by 8 x 10^6 can be simplified as (9 x 8) x (10^4 x 10^6) = 72 x 10^(4+6) = 72 x 10^10.
Now, we need to write the answer in scientific notation. In scientific notation, we represent a number in the form a x 10^b, where a is a number between 1 and 10, and b is an integer.
The answer, 72 x 10^10, can be written as 7.2 x 10^11 by moving the decimal point one place to the left.
Answer: C. 7.2 x 10^11
3. When multiplying two terms with the same base, we can simplify the expression by adding their exponents.
Therefore, 6^a x 6^v can be simplified as 6^(a+v).
Answer: A. 6^(a+v)
4. Similar to the previous question, when multiplying two terms with the same base, we can simplify the expression by adding their exponents.
Therefore, 7^5 x 7^6 can be simplified as 7^(5+6) = 7^11.
Answer: D. 7^11