Question

Use the Product Rule of Exponents to simplify the expression 7^5 ⋅7^2

Answer 1

Find the numerical equivalent of 7^2⋅7^3

Answer 2

Find the numerical equivalent of 3^9⋅3^−5

Answer 3

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.

Answer 4

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.

Answer 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.