Use the Product Rule of Exponents to simplify the expression 7^5 ⋅7^2
To simplify the expression 7^5 ⋅7^2 using the Product Rule of Exponents, we use the property that states a^m ⋅ a^n = a^(m + n).
So, in this case, we can add the exponents of 7 to get:
7^5 ⋅7^2 = 7^(5 + 2) = 7^7
Therefore, the simplified expression is 7^7.
Find the numerical equivalent of 7^2⋅7^3
To find the numerical equivalent of 7^2⋅7^3, we use the property that states a^m ⋅ a^n = a^(m + n).
So, in this case, we can add the exponents of 7 to get:
7^2⋅7^3 = 7^(2 + 3) = 7^5
Therefore, the numerical equivalent of 7^2⋅7^3 is 7^5. Now, we can evaluate 7^5 to find the answer:
7^5 = 7 × 7 × 7 × 7 × 7 = 16807
Therefore, the numerical equivalent of 7^2⋅7^3 is 16807.
Find the numerical equivalent of 3^9⋅3^−5
To find the numerical equivalent of 3^9⋅3^(-5), we use the property that states a^m ⋅ a^n = a^(m + n) and the property a^-n = 1/a^n.
First, let's simplify the exponent of 3^(-5):
3^(-5) = 1/3^5 = 1/ (3 × 3 × 3 × 3 × 3) = 1/243.
Now we have:
3^9⋅3^(-5) = 3^(9+(-5)) = 3^4 = 3 × 3 × 3 × 3 = 81.
Therefore, the numerical equivalent of 3^9⋅3^(-5) is 81.
The Product Rule of Exponents states that when multiplying two powers with the same base, we simply add their exponents.
In this case, we have 7^5 multiplied by 7^2.
To simplify, we add the exponents: 5 + 2 = 7.
Therefore, the expression 7^5 ⋅7^2 simplifies to 7^7.
To simplify the expression 7^5 ⋅ 7^2 using the Product Rule of Exponents, we need to combine the exponential expressions with the same base by adding the exponents.
According to the Product Rule of Exponents, when multiplying powers with the same base, we add the exponents.
So, in this case, we will add the exponents of 7.
7^5 ⋅ 7^2 = 7^(5 + 2)
Simplifying the exponent, we get:
7^(5 + 2) = 7^7
Therefore, the simplified expression is 7^7.