Describe how to simplify the expression 3^-6/3^-4

a. divide the bases and then add the exponents.
b. keep the base the same and then add the exponents.
c. multiply the bases and then subtract the exponents.
d. keep the base the same and then subtract the exponents.

(D)

Step-by-step explanation:

We have to simplify the given expression that is :

Now, keeping the base same and then subtracting the components, we have

first keep the base same,

Now, subtract the exponents,

⇒

⇒

Which is the required simplified expression.

Therefore, Option D is correct.

d. Keep the base the same and then subtract the exponents.

Step-by-step explanation:

The given expression:

According to the law of exponents in division with same base:-

In the given expression, both numerator and denominator has exponents wth the same base, hence to solve the expression we need to use law of exponents of division.

Hence, to simplify the , we need to keep the base the same and then subtract the exponents.

i.e

what i would say the best answer is a. 40.5

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4