Questions: If (2^*)(2^4)=8 what value x+y

Solution Steps

To solve the equation \((2^{_})(2^{4}) = 8\), we need to determine the value of the exponent represented by the asterisk. We know that \(2^4 = 16\), so we can rewrite the equation as \(2^{_} \times 16 = 8\). By dividing both sides by 16, we can solve for \(2^{*}\). Once we find the value of the exponent, we can determine the sum \(x + y\) if \(x\) and \(y\) are the exponents.

1. Rewrite the equation to isolate \(2^{*}\).
2. Solve for the exponent by equating powers of 2.
3. Determine the sum of the exponents \(x + y\).

We start with the equation given in the problem: \[ (2^{_})(2^{4}) = 8 \] This can be rewritten using the properties of exponents: \[ 2^{_ + 4} = 8 \]

Next, we express 8 as a power of 2: \[ 8 = 2^{3} \] Thus, we can equate the exponents: \[

• • 4 = 3 \]

Now, we solve for the exponent \( * \): \[

• = 3 - 4 = -1 \]

In this context, we have \( x = -1 \) and \( y = 4 \). Therefore, we calculate: \[ x + y = -1 + 4 = 3 \]

Final Answer