If c is a number with no exponent, what is the value of c in the equation below?\frac{ {4}^(7) }{ {4}^(3) } = {a}^(b) = c

Question

If c is a number with no exponent, what is the value of c in the equation below?
`\frac{ {4}^(7) }{ {4}^(3) } = {a}^(b) = c`

Answer 1

c = 256

Step-by-step explanation:

Given the equation:

`\frac{ {4}^(7) }{ {4}^(3) }={a}^b=c`

We apply the division law of indices to obtain:

`\frac{ {4}^(7) }{ {4}^(3) }={4^(7-3)=4^4=256}`

The value of c is 256.