Question

Put the expressions in order from the least to greatest

Answer 1

Explanation:

`{ ({4}^( - 4) )}^(3) \\ = {4}^( - 12)`

`\frac{ {4}^(15) }{ {4}^(5) } \\ = {4}^(10)`

`{4}^( - 5) * {4}^( - 4) \\ = {4}^( - 9)`

`\frac{1}{ {4}^( - 12) } \\ = {4}^(12)`

least to greatest

`1)\: {4}^( - 12) \\ 2) \: {4}^( - 9) \\ 3) \: {4}^(10 ) \\ 4) \: {4}^(12)`

#CMIIW

Answer 2

Ordering the expressions from least to greatest: 1.
`\( 4^(-9) \)`, 2.
`\( 4^(-12) \)`, 3.
`\( (4^(10))/(4^(-9)) \)`, 4.
`\( 4^(12) \)`

Let's simplify each expression to compare them:

1.
`\( (4^(-4))^3 \)` can be simplified by multiplying the exponents:
`\( 4^(-12) \)`.

2.
`\( (4^(15))/(4^5) \)` can be simplified by subtracting the exponents in the denominator from the exponents in the numerator:
`\( 4^(15-5) = 4^(10) \)`.

3.
`\( 4^(-4) \cdot 4^(-5) \)` can be simplified by adding the exponents:
`\( 4^(-9) \)`.

4.
`\( (1)/(4^(-12)) \)` can be simplified by changing the reciprocal and sign of the exponent:
`\( 4^(12) \)`.

Now, let's order them from least to greatest:

1.
`\( 4^(-9) \)`

2.
`\( 4^(-12) \)`

3.
`\( (4^(10))/(4^(-9)) \)`

4.
`\( 4^(12) \)`