Question

Use the multiplication property of exponents to determine if each statement is true or false.

a^4 × a^3 × a = a^7

5^2 × 3^4 = 15^6

x^6 × x^0 × x^2 × x^3 = x^11

7m^2 × 2m × 4m^5 = 56m^8

Answer 1

1)
LHS:

`{a}^(4) * {a}^(3) * a \\ = {a}^(4 + 3 + 1) \\ = {a}^(7)`
LHS = RHS. So, the statement is true

2)
LHS:

`{5}^(2) * {3}^(4) \\ = 25 * 81 \\ = {5}^(2) * {9}^(2) \\ = {45}^(2)`
LHS not equal to RHS. So, the statement is false

3)
LHS:

`{x}^(6) * {x}^(0) * {x}^(2) * {x}^(3) \\ = {x}^(6 + 0 + 2 + 3) \\ = {x}^(11)`
LHS = RHS. So, the statement is true.

4)
LHS:

`7 {m}^(2) * 2m * 4 {m}^(5) \\ = (7 * 2 * 4) {m}^(2 + 1 + 5) \\ = 56 {m}^(8)`
LHS = RHS. So, the statement is true.