Multiply. Write the result in scientific notation.
(2.3 • 101)(7 • 106)
A. 1.61 • 107
B. 1.61 • 108
C. 9.3 • 106
D. 9.3 • 107
The product of the numbers is:
(2.3 • 101)(7 • 106) = 16.1 • 107
But we want to write this in scientific notation, which means expressing it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point to the left one place, and adding 1 to the exponent:
1.61 • 108
Therefore, the answer is B. 1.61 • 108.
(2.2 ∙ 10–3)(4 ∙ 10–2)
A. 2.2 ∙ 106
B. 2.2 ∙ 10–5
C. 8.8 ∙ 106
D. 8.8 ∙ 10–5
When multiplying numbers in scientific notation, we can multiply the coefficients (the non-exponential parts) and add their exponents. Using this rule, we get:
(2.2 ∙ 10–3)(4 ∙ 10–2) = (2.2 * 4) * 10^(-3-2) = 8.8 * 10^-5
Therefore, the answer is D. 8.8 ∙ 10–5.
Simplify the expression.
7t4 ∙ 7t4
A. 49t8
B. 14t4
C. 49t16
D. 14t8
When multiplying two expressions with the same base, we can add their exponents. In this case, both expressions have a base of 7t, so we can add their exponents to get:
7t4 ∙ 7t4 = 7^(1+1) * t^(4+4) = 49t^8
Therefore, the answer is A. 49t8.
Simplify the expression.
–x(7x – 8)
A. 6x2 – 9x
B. –7x – 8x
C. –7x2 + 8x
D. 7x + 8x
When multiplying two terms, we can use the distributive property, which means we multiply each term inside the parentheses by the term outside the parentheses. In this case, we have:
-x(7x – 8) = -x * 7x + (-x) * (-8)
Simplifying, we get:
-x * 7x = -7x^2
-x * (-8) = 8x
Putting it all together, we get:
-x(7x – 8) = -7x^2 + 8x
Therefore, the answer is C. –7x2 + 8x.
Simplify the expression.
5k2(–6k2 – 2k + 6)
A. –30k3 + 3k2 + 30k
B. 30k4 – 10k3 + 11k2
C. –k4 + 3k3 + 11k2
D. –30k4 – 10k3 + 30k2
When using the distributive property to simplify this expression, we will multiply 5k^2 by each term inside the parentheses. We get:
5k^2(-6k^2 - 2k + 6) = (-30k^4 - 10k^3 + 30k^2)
Therefore, the answer is D. –30k^4 – 10k^3 + 30k^2.
Simplify the expression.
(2k + 1) (k – 4)
A. 2k2 – 7k + 4
B. 2k2 –3k + 4
C. 2k2 + 9k + 4
D. 2k2 – 7k – 4