Use the Product Rule of Exponents to simplify the expression 38 ⋅33.(1 point)
The Product Rule of Exponents states that when multiplying two powers with the same base, you add the exponents.
In this case, you have 38 ⋅ 33.
The base is 3, so the exponents are 8 and 3.
Using the Product Rule of Exponents, you add the exponents:
38 ⋅ 33 = 3^(8+3) = 3^11
Use the Product Rule of Exponents to simplify the expression 75 ⋅72.(1 point)
The Product Rule of Exponents states that when multiplying two powers with the same base, you add the exponents.
In this case, you have 75 ⋅ 72.
The base is 7, so the exponents are 5 and 2.
Using the Product Rule of Exponents, you add the exponents:
75 ⋅ 72 = 7^(5+2) = 7^7
Find the numerical equivalent of 72⋅73(1 point)
To find the numerical equivalent of 72⋅73, you simply need to multiply 72 and 73.
72 × 73 = 5256
Therefore, the numerical equivalent of 72⋅73 is 5256.
Find the numerical equivalent of 7^2⋅7^3(1 point)
To find the numerical equivalent of 7^2⋅7^3, you can use the product rule of exponents, which states that when multiplying powers with the same base, you add the exponents.
In this case, the base is 7, and the exponents are 2 and 3.
Using the product rule of exponents, you add the exponents:
7^2⋅7^3 = 7^(2+3) = 7^5
To find the numerical equivalent, you evaluate 7^5:
7^5 = 7 × 7 × 7 × 7 × 7 = 16807
Therefore, the numerical equivalent of 7^2⋅7^3 is 16807.
Find the numerical equivalent of 39⋅3−5(1 point)
To find the numerical equivalent of 39⋅3^-5, we need to evaluate the expression.
First, we need to find the value of 3^-5.
Recall that a negative exponent means to take the reciprocal of the base raised to the positive exponent.
In this case, 3^-5 can be written as 1/(3^5).
Now, let's calculate the value of 3^5:
3^5 = 3 × 3 × 3 × 3 × 3 = 243.
Therefore, 3^-5 is equal to 1/243.
Now, we can substitute this value back into the original expression:
39 ⋅ 3^-5 = 39 ⋅ (1/243).
To calculate this, we can multiply 39 by 1 and then divide the result by 243:
(39/1) ÷ 243 = 39/243.
We can simplify this fraction further by dividing the numerator and denominator by their greatest common divisor:
39/243 = (3 × 13)/(3 × 3 × 3 × 3 × 3) = 13/81.
Therefore, the numerical equivalent of 39⋅3^-5 is 13/81.