What is the expression for f(x) when we rewrite 3^(5x+3)*27^(x) as 3^(f(x)) ? f(x)=

Rewrite 27 as power of 3: We need to express the product of two powers of 3 as a single power of 3. The given expression is 3^(5x+3) * 27^(x). We know that 27 is a power of 3, specifically 27 = 3^3. So, we can rewrite 27^(x) as (3^3)^(x).Apply power of a power rule: Now we apply the power of a power rule, which states that (a^b)^c = a^(b*c). So, (3^3)^(x) becomes 3^(3*x) or 3^(3x).Multiply expressions with same base: Next, we multiply the two expressions with the same base by adding their exponents. The expression becomes 3^(5x+3) * 3^(3x). According to the laws of exponents, a^(m) * a^(n) = a^(m+n). So, we add the exponents 5x+3 and 3x together.Combine like terms: Adding the exponents gives us 3^(5x+3+3x). We combine like terms to simplify the exponent: 5x + 3x = 8x and 3 remains unchanged.Simplify the exponent: The simplified exponent is 8x + 3. Therefore, the expression 3^(5x+3) * 27^(x) can be rewritten as 3^(8x+3).Set f(x) equal to exponent: Since we want to express this as 3^(f(x)), we set f(x) equal to the exponent we found. So, f(x) = 8x + 3.

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What is the expression for
f(x) when we rewrite
3^(5x+3)*27^(x) as
3^(f(x)) ?

f(x)=

What is the expression for $f(x)$ when we rewrite $3^{5 x+3} \cdot 27^{x}$ as $3^{f(x)}$ ? $\newline$ $f(x)=$

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Algebra 2

Evaluate exponential functions

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Q. What is the expression for

f(x)

when we rewrite

3^{5 x+3} \cdot 27^{x}

3^{f(x)}

\newline

f(x)=

Rewrite $27$ as power of $3$ : We need to express the product of two powers of $3$ as a single power of $3$ . The given expression is $3^{5x+3} \times 27^{x}$ . We know that $27$ is a power of $3$ , specifically $27 = 3^3$ . So, we can rewrite $27^{x}$ as $(3^3)^{x}$ .
Apply power of a power rule: Now we apply the power of a power rule, which states that $(a^b)^c = a^{(b*c)}$ . So, $(3^3)^{x}$ becomes $3^{(3*x)}$ or $3^{3x}$ .
Multiply expressions with same base: Next, we multiply the two expressions with the same base by adding their exponents. The expression becomes $3^{5x+3} \times 3^{3x}$ . According to the laws of exponents, $a^{m} \times a^{n} = a^{m+n}$ . So, we add the exponents $5x+3$ and $3x$ together.
Combine like terms: Adding the exponents gives us $3^{5x+3+3x}$ . We combine like terms to simplify the exponent: $5x + 3x = 8x$ and $3$ remains unchanged.
Simplify the exponent: The simplified exponent is $8x + 3$ . Therefore, the expression $3^{5x+3} \times 27^{x}$ can be rewritten as $3^{8x+3}$ .
Set $f(x)$ equal to exponent: Since we want to express this as $3^{f(x)}$ , we set $f(x)$ equal to the exponent we found. So, $f(x) = 8x + 3$ .