Use the product rule of exponents to simplify the expression 13^10 * 13^4.
responses
a. 13^14
b. 13^40
c. 169^14
d. 169^40
I apologize for the mistake. Let's correct it.
To find the numerical equivalent of 8^1 * 8^3, we multiply the bases (8) and add the exponents (1 + 3 = 4). So, 8^1 * 8^3 = 8^(1 + 3) = 8^4.
The numerical equivalent of 8^1 * 8^3 is 8^4, which is equal to 4,096.
Therefore, the correct answer is:
b. 4,096
Certainly! Let's double-check the answer.
To simplify k^120/k^30, we can subtract the exponents in the numerator and denominator. So, we have k^(120-30) = k^90.
Therefore, the correct answer is:
b. k^90
After reviewing it again, the correct answer is indeed b. k^90.
To find the missing number in the simplified exponential expression 15^? / 15^7 = 15^12, we can use the quotient rule of exponents. According to the quotient rule, when dividing two exponential expressions with the same base, we subtract the exponents. So, we have 15^(? - 7) = 15^12.
To make the exponent on the left side of the equation match the exponent on the right side, we need to set ? - 7 equal to 12. Solving for ?, we find that ? = 12 + 7 = 19.
Therefore, the correct answer is:
d. 19
The value of any number raised to the power of 0 is always 1. Therefore, (8.2)^0 = 1.
So, the expression (8.2)^0 + 4.3 simplifies to 1 + 4.3 = 5.3.
Therefore, the correct answer is:
c. 5.3
Any non-zero number raised to the power of 0 is always 1. Thus, (1/4)^0 = 1.
Therefore, the expression 13 - (1/4)^0 simplifies to 13 - 1 = 12.
Therefore, the correct answer is:
d. 12
To find the expression that is equal to 193^0 + 4/3 (10 - 7 * 4^0), we need to simplify each part of the expression.
First, any number (except for 0) raised to the power of 0 is always 1. Hence, 193^0 = 1.
Next, let's simplify the other part of the expression: 4/3 (10 - 7 * 4^0). Since exponentiation takes precedence over multiplication and multiplication takes precedence over addition and subtraction, the order of operations dictates that we first evaluate the exponentiation (4^0) which equals 1. So, 4/3 (10 - 7 * 4^0) simplifies to 4/3 (10 - 7 * 1) = 4/3 (10 - 7) = 4/3 (3) = 12/3 = 4.
Adding the simplified parts together, 193^0 + 4 equals 1 + 4 = 5.
Therefore, the correct answer is:
c. 5
To simplify the expression (7^3)^9 using the power rule of exponents, we multiply the exponents together. Thus, we have 7^(3*9) = 7^27.
Therefore, the correct answer is:
a. 7^27
To simplify the expression (24^2)^5 using the power rule of exponents, we multiply the exponents together. Thus, we have 24^(2*5) = 24^10.
Therefore, the correct answer is:
a. 24^10
To simplify the expression 13^10 * 13^4 using the product rule of exponents, we add the exponents together. Thus, we have 13^(10+4) = 13^14.
Therefore, the correct answer is:
a. 13^14
An expression was simplified to 24^12. which expression correctly used the product rule of exponents to simplify?
responses
a. 12^4 * 12^8
b. 24^3 * 24^4
c. 24^4 * 24^8
d. 6^4 * 4^3