Question

4 to the power of 3 times 4 to the power of -6 = 4 to the power of 5 times 4 to the power of x. What does x equal?

Answer 1

x = -8

Explanation:

First, let's turn this word problem into an equation:

4 to the power of 3 (4^3) times (x) 4 to the power of -6 (4^-6) equals (=) 4 to the power of 5 (4^5) times (x) 4 to the power of x (4^x)

4^3 x 4^-6 = 4^5 x 4^X

Now, let's solve:

Multiplying powers with the same base, you can just add the powers together:

4^3 x 4^-6

3 + ( -6 ) = -3

4^-3 = 4^5 x 4^X

Let's make this easier since all the bases are the same:

-3 = 5 + x

Subtract 5 from each side:

-3 = 5 + x

-5 + ( -3 ) = x

-8 = x

Let's check:

4^3 x 4^-6 = 4^5 x 4^X

Substitute -8 in for x:

4^3 x 4^-6 = 4^5 x 4^-8

Since all bases are the same, add together the powers:

4^-3 = 4^-3

Answer 2

x=-8

Explanation:

first we calculate the product

4^-3=4^x+5

since the bases are the same we set the exponents..

-3=x+5

then we move the x to the opposite side and -3 to the opposite site

-x=5+3

then we add the numbers

-x=8

then we change the signs

x=-8