Use the Product Rule of Exponents to simplify the expression 7^5 ⋅7^2.(1 point)

Answer 1

Using the Product Rule of Exponents, we add the exponents when multiplying the same base.

So, we add the exponents 5 and 2 to get 7.

Therefore, 7^5 ⋅7^2 simplifies to 7^7.

Answer 2

Find the numerical equivalent of 7^2⋅7^3(1 point)

Answer 3

To find the numerical equivalent of 7^2⋅7^3, we simplify each exponent and then multiply the resulting values.

7^2 = 7 * 7 = 49

7^3 = 7 * 7 * 7 = 343

Multiplying these values together, we have:

49 * 343 = 16,807

So, the numerical equivalent of 7^2⋅7^3 is 16,807.

Answer 4

Find the numerical equivalent of 3^9⋅3^−5(1 point)

Answer 5

To find the numerical equivalent of 3^9⋅3^−5, we simplify the exponents and perform the multiplication.

3^9 can be written as:

3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 19,683

3^(-5) is the reciprocal of 3^5, which can be written as:

(1/3) * (1/3) * (1/3) * (1/3) * (1/3) = 1/243

Multiplying these values together, we have:

19,683 * 1/243 = 81

So, the numerical equivalent of 3^9⋅3^−5 is 81.