Question

Determine the value of the variable in each expression:

93
A){1}/{m}
B){(11)^c}/{(11)^2}

Answer 1

The variables are

A) m = 1/93

B) c = -2

Step-by-step explanation:

To determine the value of the variable m in expression A, we can set up the equation
`\( (1)/(m) = 93 \)`. Multiplying both sides by m to isolate m gives us 1 = 93m , and dividing both sides by 93 yields
`\( m = (1)/(93) \)`.

For expression B, we have
`\( ((11)^c)/((11)^2) \)`. Since the bases are the same, we can equate the exponents: c = 2 for the expression to hold true. However, it's essential to notice that the exponent c represents the power to which 11 must be raised to obtain the numerator. Therefore, c = -2 because
`\( (11)^(-2) = (1)/((11)^2) \).`

Understanding exponent rules and their applications in algebraic expressions can provide valuable insights into solving equations involving variables.