Question

Name Yala. Al Write down each of the following expressions in the form of a power of one number a) 5³x5⁴ b) (-7)² ×(-7)³ c) 3⁶x3³ d) 27⁰x27² e) (-2)² ×(-2)³ × (-2)⁴ f) 3⁴x9²x(-3)⁶ g) (-4)⁶ × (-4)⁵ (-4)³ h) (-8)x(-8)x2² i) (0.25)×(0.25)⁴ × (0.25)⁰ J) 7³x7²x7​

Answer 1

A.
`{5}^(7)`

B.
`( { - 7})^(5)`

C.
`{3}^(9)`

D.
`{27}^(2)`

E.
`({ - 2})^(9)`

F.
`{3}^(14)`

G.
`{( - 4)}^(14)`

H.
`{2}^(8)`

I.
`{(0.25)}^(5)`

J.
`{7}^(6)`

Explanation:

A.

`{5}^(3) * {5}^(4) \\ = {5}^(3 + 4) \\ = {5}^(7)`

B.

`( { - 7})^(2) * ( { - 7})^(3) \\ = ( { - 7})^(2 + 3) \\ = ( { - 7})^(5)`

C.

`{3}^(6) * {3}^(3) \\ = {3}^(6 + 3) \\ = {3}^(9)`

D.

`{27}^(0) * {27}^(2) \\ = {27}^(0 + 2) \\ = {27}^(2)`

E.

`( { - 2})^(2) * ( { - 2})^(3) * ( { - 2})^(4) \\ = ( { - 2})^(2 + 3 + 4) \\ = ({ - 2})^(9)`

F.

`{3}^(4) * {9}^(2) * ( { - 3})^(6) \\ = {3}^(4) * {3}^(2 * 2) * {3}^(6) \\ = {3}^(4) * {3}^(4) * {3}^(6) \\ = {3}^(4 + 4 + 6) \\ = {3}^(14)`

G.

`{( - 4)}^(6) * {( - 4)}^(5) * {( - 4)}^(3) \\ = {( - 4)}^(6 + 5 + 3) \\ = {( - 4)}^(14)`

H.

`( - 8) * ( - 8) * {2}^(2) \\ = 8 * 8 * {2}^(2) \\ = {2}^(3) * {2}^(3) * {2}^(2) \\ = {2}^(3 + 3 + 2) \\ = {2}^(8)`

I.

`0.25 * {(0.25)}^(4) * {(0.25)}^(0) \\ = {(0.25)}^(1) * {(0.25)}^(4) * {(0.25)}^(0) \\ = * {(0.25)}^(1+4+0) \\ = * {(0.25)}^(5)`

J.

`{7}^(3) * {7}^(2) * 7 \\ = {7}^(3) * {7}^(2) * {7}^(1) \\ = {7}^(3+2+1) \\ = {7}^(6)`