Question

Put the expressions in order from least to greatest.

Answer 1

Answer:

$\frac{11^{4} }{11^{11} } ,\frac{1}{11^{-4} }, 11^{5}*11^{2}, (11^{-3})^{-3}$

Step-by-step explanation:

For this, you need to know the rules of exponents:

If the coefficient is the same, you can do things to it (which I will get into)

In this case, all the coefficients are 11, so we don't have to worry about the coefficients being different.

For the first one, you can subtract the denominator exponent by the numerator exponent like so:

$11^{4} * 11^{-11} = 11^{-7}$

(When you multiply, you add the exponents)

Also, the rule is: $x^{-y} = \frac{1}{x^{y} }$ or $\frac{1}{x^{-y} } = x^{y}$

For the second one, you can use the rule mentioned before:

$\frac{1}{11^{-4} } = 11^{4}$

For the third one, you want to multiply the exponents (in these kinds of cases, you can multiply the exponent by the exponent)

So:

$(11^{-3} )^{-3} = 11^{9}$

Finally, the fourth one, you can simply just add the exponents:

$11^{5} * 11^{2} = 11^{7}$

Then, just order them from least to greatest by their exponents value :)