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Select the expressions that are equivalent to $5f + 3f$ . $\newline$ Multi-select Choices: $\newline$ (A) $2f + 6f$ $\newline$ (B) $f^8$ $\newline$ (C) $f + 8$ $\newline$ (D) $7f$

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Operations with rational exponents

Full solution

Q. Select the expressions that are equivalent to

5f + 3f

.

\newline

Multi-select Choices:

\newline

(A)

2f + 6f

\newline

(B)

f^8

\newline

(C)

f + 8

\newline

(D)

7f

Simplify expression: Simplify the expression $5f + 3f$ . Combine like terms by adding the coefficients of $f$ . $5f + 3f = 8f$
Combine like terms: Compare the simplified expression $8f$ to the multi-select choices. $\newline$ (A) $2f + 6f$ simplifies to $8f$ . $\newline$ $2f + 6f = 8f$
Compare with choices: Check if choice (B) $f^8$ is equivalent to $8f$ . $f^8$ represents $f$ raised to the power of $8$ , not $8$ times $f$ . This is not equivalent to $8f$
Check choice (B): Check if choice (C) $f + 8$ is equivalent to $8f$ . $f + 8$ represents $1f$ plus $8$ , not $8$ times $f$ . This is not equivalent to $8f$
Check choice (C): Check if choice (D) $7f$ is equivalent to $8f$ . $\newline$ $7f$ represents $7$ times $f$ , which is not equal to $8$ times $f$ . $\newline$ This is not equivalent to $8f$

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