What's four to the six power times four to the seventh power

67,108,864 or 4^13

Step-by-step explanation:

4^6*4^7=4^13 you basically just add the exponents since the base is the same.

Since these two powers have the same base of 4, you can multiply

them together by simply adding their exponents to get 4¹³.

This idea is called the product rule.

A common mistake in this problem would be to multiply

the bases together and give an answer of 16¹³.

It's important to understand however that the 4's in this problem can't

be multiplied together because they're not coefficients, they're bases.

When applying your exponent rules, your base will never change.

check the picture below.

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