What is the value of A when we rewrite 4^(x+3)-4^(x) as A*4^(x) ? A=

Recognize Property of Exponents: We need to factor out 4^(x) from the expression 4^(x+3) - 4^(x). To do this, we recognize that 4^(x+3) can be written as 4^(x)*4^(3) because of the property of exponents that states a^(m+n) = a^(m)*a^(n).Rewrite Using Property: Now we rewrite the expression using this property: 4^(x+3) - 4^(x) = 4^(x)*4^(3) - 4^(x). We can factor 4^(x) out of both terms to get 4^(x) * (4^(3) - 1).Calculate Result: We calculate 4^(3) - 1. Since 4^(3) is 4*4*4, which equals 64, we have 64 - 1 = 63.Substitute Result: Now we substitute this result back into the factored expression: 4^(x) * (4^(3) - 1) becomes 4^(x) * 63.Identify Value of A: We can see that the expression 4^(x) * 63 is in the form of A*4^(x), which means A is equal to 63.

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What is the value of
A when we rewrite
4^(x+3)-4^(x) as
A*4^(x) ?

A=

What is the value of $A$ when we rewrite $4^{x+3}-4^{x}$ as $A \cdot 4^{x}$ ? $\newline$ $A=$

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. What is the value of

A

when we rewrite

4^{x+3}-4^{x}

A \cdot 4^{x}

\newline

A=

Recognize Property of Exponents: We need to factor out $4^{x}$ from the expression $4^{x+3} - 4^{x}$ . To do this, we recognize that $4^{x+3}$ can be written as $4^{x}\cdot4^{3}$ because of the property of exponents that states $a^{m+n} = a^{m}\cdot a^{n}$ .
Rewrite Using Property: Now we rewrite the expression using this property: $4^{(x+3)} - 4^{x} = 4^{x}\cdot4^{3} - 4^{x}$ . We can factor $4^{x}$ out of both terms to get $4^{x} \cdot (4^{3} - 1)$ .
Calculate Result: We calculate $4^{3} - 1$ . Since $4^{3}$ is $4\times4\times4$ , which equals $64$ , we have $64 - 1 = 63$ .
Substitute Result: Now we substitute this result back into the factored expression: $4^{x} \times (4^{3} - 1)$ becomes $4^{x} \times 63$ .
Identify Value of A: We can see that the expression $4^{x} \times 63$ is in the form of $A\times4^{x}$ , which means $A$ is equal to $63$ .