11. Which of the following expressions is true?
A. 4^3 * 4^4 = 4^12
B. 5^2 * 5^3 > 5^5
C. 3^2 * 3^5 > 3^10
D. 5^2 * 5^4 < 5^8
12. Which of the following expressions true?
A. 2^4 * 2^3 = 2^12
B. 3^3 * 3^6 > 3^8
C. 4^2 * 4^2 > 4^4
D. 5^5 * 5^2 = 5^10
I think 11. Is D, and 12. Is B.
Can you please check my answers?
5⁸>5⁶✓
3⁹>3⁸✓
You picked the right option
Thank you
5^2 x 5^4 =5^8 T or F
True.
When you multiply two powers with the same base, you add the exponents.
So,
5^2 * 5^4 = 5^(2+4) = 5^6
Therefore, 5^2 * 5^4 is not equal to 5^8. But, 5^2 * 5^4 = 5^8 is true.
4^4*4^4=4^16 T or F
True.
When you multiply two powers with the same base, you add the exponents.
So,
4^4 * 4^4 = 4^(4+4) = 4^8
However, 4^8 is not equal to 4^16.
Therefore, the statement "4^4*4^4=4^16" is false.
8^3*8^2<8^4 T or F
True.
When you multiply two powers with the same base, you add the exponents.
So,
8^3 * 8^2 = 8^(3+2) = 8^5
However, 8^5 is not greater than 8^4.
Therefore, the statement "8^3*8^2<8^4" is true.
what is the value of the expression 4^5/4^5
The value of the expression 4^5/4^5 is 1.
When you divide two powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
So,
4^5/4^5 = 4^(5-5) = 4^0
And any number (except 0) raised to the power of 0 is 1. Therefore, 4^0 = 1.
Hence, the value of the expression 4^5/4^5 is 1.
what is the value 4^7/4^9
When you divide two powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
So,
4^7/4^9 = 4^(7-9) = 4^(-2)
Now, we know that a negative exponent indicates that the number should be written as a reciprocal.
So,
4^(-2) = 1/4^2 = 1/16
Therefore, the value of the expression 4^7/4^9 is 1/16.
(m^2-m-3) + (m-4)
First, combine like terms by adding the coefficients of m and the constants:
(m^2 - m - 3) + (m - 4) = m^2 - m + m - 3 - 4
Simplify by adding -3 and -4:
m^2 - 2 - m
Therefore, the simplified form of (m^2-m-3) + (m-4) is m^2 - 2 - m.
nope
I apologize and thank you for pointing that out. Let me try again.
(m^2 - m - 3) + (m - 4)
= m^2 - m - 3 + m - 4 (Distribute the addition sign)
= m^2 - m + m - 3 - 4 (Rearrange the terms)
= m^2 - 7 (Combine the constants)
Therefore, the simplified form of (m^2-m-3) + (m-4) is m^2 - 7.
how about (7x^2-x-2
I am sorry for my mistake. I missed closing the parenthesis in my previous response.
The expression (7x^2-x-2) cannot be simplified as it is already in its simplest form.
If there was an operator (+, -, *, /, etc.) followed by another expression, then we could simplify it further.
how about (7x^2-x-2) - (-6x^3+3)
To simplify, we need to distribute the negative sign to each term inside the parentheses:
(7x^2 - x - 2) - (-6x^3 + 3) = 7x^2 - x - 2 + 6x^3 -3
Now, we can combine like terms by adding the coefficients of x^2, x, and the constants:
7x^2 - x - 2 + 6x^3 - 3 = 6x^3 + 7x^2 - x - 5
Therefore, the simplified form of (7x^2 - x - 2) - (-6x^3 + 3) is 6x^3 + 7x^2 - x - 5.
Suppose you earned 7t - 1 dollars on Monday and 8t + 5 dollars on Tuesday. What were your total earnings? Simplify your answer.
To find the total earnings, we need to add the earnings from both days:
Total earnings = Monday's earnings + Tuesday's earnings
Total earnings = (7t - 1) + (8t + 5)
Next, we can simplify this expression by combining like terms:
Total earnings = 7t + 8t - 1 + 5 (Distribute the addition sign)
Total earnings = 15t + 4 (Combine the constants)
Therefore, the total earnings are 15t + 4 dollars.
Multiply. Write the result in the scientific notation (1.4 x 10^1)(8 x 10^4)
When multiplying numbers written in scientific notation, we multiply the coefficients and add the exponents of 10.
(1.4 x 10^1)(8 x 10^4) = 1.4 * 8 * 10^(1+4)
= 11.2 * 10^5
To write the result in scientific notation, we need to adjust the coefficient of 11.2 to be between 1 and 10. Here, we can write 11.2 as 1.12 x 10^1.
Therefore,
(1.4 x 10^1)(8 x 10^4) = 11.2 x 10^5 = 1.12 x 10^6 (in scientific notation)
do the same thing for (2.2 x 10^-3)(4 x 10^-2)
When multiplying numbers written in scientific notation, we multiply the coefficients and add the exponents of 10.
(2.2 x 10^-3)(4 x 10^-2) = 2.2 * 4 * 10^(-3-2)
= 8.8 * 10^-5
To write the result in scientific notation, we need to adjust the coefficient of 8.8 to be between 1 and 10. Here, we can write 8.8 as 8.8 x 10^(-1).
Therefore,
(2.2 x 10^-3)(4 x 10^-2) = 8.8 x 10^-5 = 8.8 x 10^(-1 - 4) (in scientific notation)
simplify 8t^5 x 8t^5
When multiplying two terms with the same base, we add their exponents.
So,
8t^5 x 8t^5 = (8 x 8) t^(5+5)
= 64t^10
Therefore, 8t^5 x 8t^5 simplifies to 64t^10.
simplify -x(7x-8)
To simplify the expression -x(7x - 8), we need to distribute the negative sign to each term inside the parentheses:
-x(7x - 8) = -x(7x) + x(8)
Now we can simplify by multiplying -x with 7x and with 8:
-x(7x) + x(8) = -7x^2 + 8x
Therefore, -x(7x - 8) simplifies to -7x^2 + 8x.
simplify 3k^2(-2k^2-4k+7)
To simplify the expression 3k^2(-2k^2 - 4k + 7), we need to distribute 3k^2 to each term inside the parentheses:
3k^2(-2k^2 - 4k + 7) = -6k^4 - 12k^3 + 21k^2
Therefore, 3k^2(-2k^2 - 4k + 7) simplifies to -6k^4 - 12k^3 + 21k^2.
simplify (3k+2)(k-3)
To simplify the expression (3k + 2)(k - 3), we need to use the distributive property:
(3k + 2)(k - 3) = 3k(k - 3) + 2(k - 3)
Now let's simplify by doing the multiplication:
3k(k - 3) + 2(k - 3) = 3k^2 - 9k + 2k - 6
Finally, we can combine like terms:
3k^2 - 7k - 6
Therefore, (3k + 2)(k - 3) simplifies to 3k^2 - 7k - 6.
simplify (-2y+5)(y+3)
To simplify the expression (-2y + 5)(y + 3), we need to use the distributive property:
(-2y + 5)(y + 3) = -2y(y + 3) + 5(y + 3)
Now let's simplify by doing the multiplication:
-2y(y + 3) + 5(y + 3) = -2y^2 - 6y + 5y + 15
Finally, we can combine like terms:
-2y^2 - y + 15
Therefore, (-2y + 5)(y + 3) simplifies to -2y^2 - y + 15.
2^3/2^3
When you divide two powers with the same base, you need to subtract the exponent in the denominator from the exponent in the numerator.
So,
2^3/2^3 = 2^(3-3) = 2^0
And any number (except 0) raised to the power of 0 is 1. Therefore, 2^0 = 1.
Hence, the value of the expression 2^3/2^3 is 1.
4^7/4^9
When you divide two powers with the same base, you need to subtract the exponent in the denominator from the exponent in the numerator.
So,
4^7/4^9 = 4^(7-9) = 4^(-2)
Now, we know that a negative exponent indicates that the number should be written as a reciprocal.
So,
4^(-2) = 1/4^2 = 1/16
Therefore, the value of the expression 4^7/4^9 is 1/16.
(1.8•10^1)(7•10^5)
To multiply two numbers written in scientific notation, we need to multiply the coefficients and add the exponents:
(1.8•10^1)(7•10^5) = 1.8 x 7 x 10^(1+5)
= 12.6 x 10^6
To write the result in scientific notation, we need to adjust the coefficient of 12.6 to be between 1 and 10. Here, we can write 12.6 as 1.26 x 10^1.
Therefore,
(1.8•10^1)(7•10^5) = 12.6 x 10^6 = 1.26 x 10^7 (in scientific notation).
(2.2•10^-3)4•10^-2)
To multiply two numbers written in scientific notation, we need to multiply the coefficients and add the exponents:
(2.2•10^-3)(4•10^-2) = 2.2 x 4 x 10^(-3-2)
= 8.8 x 10^-5
To write the result in scientific notation, we need to adjust the coefficient of 8.8 to be between 1 and 10. Here, we can write 8.8 as 8.8 x 10^-1.
Therefore,
(2.2•10^-3)(4•10^-2) = 8.8 x 10^-5 = 8.8 x 10^(-1 - 4) (in scientific notation).