Question

What is the value of b in the equation below?

5⁶/5²=a^b.
A. 3
B. 4
C. 5
D. 8

Answer 1

The value of b in the equation 5⁶/5²=
`a^b` is 4.

Step-by-step explanation:

To find the value of b in the equation 5⁶/5²=
`a^b`, we can simplify the left-hand side first. 5⁶/5² equals 5
`^{(6-2)` which is equal to 5⁴. So the equation becomes 5⁴ =
`a^b`. To solve for b, we need to find a number that, when raised to the power of b, gives us 5⁴. Since 5⁴ equals 625, and 625 is 5² raised to the power of 2 (5² = 25, and 25² = 625), the value of b is 4.

In the equation 5⁶/5²=
`a^b`, we start by simplifying the left-hand side. Using the rule of exponents, subtracting the exponents gives us 5
`^{(6-2)`= 5⁴. This simplifies the equation to 5⁴ =
`a^b`. To find b, we need to determine what power, when applied to a, equals 5⁴. Since 5⁴ equals 625, which is the result of 5² raised to the power of 2 (5² = 25, and 25² = 625), we conclude that b equals 4.

Therefore, in the equation 5⁶/5²=
`a^b`, the value of b is 4. By simplifying the left-hand side and equating it to 5⁴, which is 625, we find that b equals 4 as 625 is the result of 5² raised to the power of 2. Thus, b must be 4 for the equation to hold true.