What is the value of A when we rewrite 2^(x-6)+2^(x) as A*2^(x) ? A=

Factor out common base: Factor out the common base of 2 raised to the power of x from both terms. We have 2^(x-6) + 2^(x). To factor out 2^(x), we need to express 2^(x-6) in terms of 2^(x). Using the property of exponents that a^(m-n) = a^m / a^n, we can write 2^(x-6) as 2^(x) / 2^6.Rewrite in terms of 2^(x): Rewrite 2^(x-6) in terms of 2^(x). 2^(x-6) = 2^(x) / 2^6 = 2^(x) * 1/2^6 = 2^(x) * 1/64 Now we can rewrite the original expression as: 2^(x-6) + 2^(x) = 2^(x) * 1/64 + 2^(x)Factor out 2^(x): Factor 2^(x) out of the expression. We can now factor 2^(x) out of both terms to get: 2^(x) * 1/64 + 2^(x) = 2^(x) * (1/64 + 1)Simplify inside parentheses: Simplify the expression inside the parentheses. 1/64 + 1 can be rewritten as 1/64 + 64/64 to have a common denominator. 1/64 + 64/64 = (1 + 64) / 64 = 65/64Combine with factored out 2^(x): Combine the simplified expression with the factored out 2^(x). Now we have: 2^(x) * (1/64 + 1) = 2^(x) * 65/64 This means that A is 65/64.

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What is the value of
A when we rewrite
2^(x-6)+2^(x) as
A*2^(x) ?

A=

What is the value of $A$ when we rewrite $2^{x-6}+2^{x}$ as $A \cdot 2^{x}$ ? $\newline$ $A=$

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Math Problems

Algebra 2

Solve exponential equations by rewriting the base

Full solution

Q. What is the value of

A

when we rewrite

2^{x-6}+2^{x}

A \cdot 2^{x}

\newline

A=

Factor out common base: Factor out the common base of $2$ raised to the power of $x$ from both terms. $\newline$ We have $2^{x-6} + 2^{x}$ . To factor out $2^{x}$ , we need to express $2^{x-6}$ in terms of $2^{x}$ . $\newline$ Using the property of exponents that $a^{m-n} = a^m / a^n$ , we can write $2^{x-6}$ as $2^{x} / 2^6$ .
Rewrite in terms of $2^{x}$ : Rewrite $2^{x-6}$ in terms of $2^{x}$ . $\newline$ $2^{x-6} = 2^{x} / 2^{6} = 2^{x} \times 1/2^{6} = 2^{x} \times 1/64$ $\newline$ Now we can rewrite the original expression as: $\newline$ $2^{x-6} + 2^{x} = 2^{x} \times 1/64 + 2^{x}$
Factor out $2^{x}$ : Factor $2^{x}$ out of the expression. $\newline$ We can now factor $2^{x}$ out of both terms to get: $\newline$ $2^{x} \times \frac{1}{64} + 2^{x} = 2^{x} \times (\frac{1}{64} + 1)$
Simplify inside parentheses: Simplify the expression inside the parentheses. $\newline$ $\frac{1}{64} + 1$ can be rewritten as $\frac{1}{64} + \frac{64}{64}$ to have a common denominator. $\newline$ $\frac{1}{64} + \frac{64}{64} = \frac{(1 + 64)}{64} = \frac{65}{64}$
Combine with factored out $2^{x}$ : Combine the simplified expression with the factored out $2^{x}$ . Now we have: $2^{x} \times (\frac{1}{64} + 1) = 2^{x} \times \frac{65}{64}$ This means that $A$ is $\frac{65}{64}$ .