Select all the expressions that are equivalent to 6^-9 * 6^2. Multi-select Choices: (A)6^-7 (B)1/6^7 (C)6^-18 (D)1/6^-7

Add Exponents: When multiplying expressions with the same base, we add the exponents. So, we have 6^-9 * 6^2 = 6^(-9 + 2). Calculate the sum of the exponents: -9 + 2 = -7.Simplify Expression: The expression simplifies to 6^-7. Check if any of the choices match this expression. (A) 6^-7 is exactly the same as our simplified expression.Check Choices: (B) 1/6^7 is the positive exponent equivalent of 6^-7 because a negative exponent indicates the reciprocal of the base raised to the positive exponent.Match Simplified Expression: (C) 6^-18 does not match our simplified expression because the exponent is -18, which is not the result of -9 + 2.(D) 1/6^-7 is not equivalent to our simplified expression because it suggests the reciprocal of 6^-7, which would be 6^7.

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Math Problems

Algebra 2

Multiply and divide rational expressions

Full solution

Q. Select all the expressions that are equivalent to

6^{-9} \times 6^2

\newline

Multi-select Choices:

\newline

(A)

6^{-7}

\newline

(B)

\frac{1}{6^7}

\newline

(C)

6^{-18}

\newline

(D)

\frac{1}{6^{-7}}

Add Exponents: When multiplying expressions with the same base, we add the exponents. So, we have $6^{-9} \times 6^{2} = 6^{(-9 + 2)}$ . $\newline$ Calculate the sum of the exponents: $-9 + 2 = -7$ .
Simplify Expression: The expression simplifies to $6^{-7}$ . Check if any of the choices match this expression. (A) $6^{-7}$ is exactly the same as our simplified expression.
Check Choices: (B) $\frac{1}{6^7}$ is the positive exponent equivalent of $6^{-7}$ because a negative exponent indicates the reciprocal of the base raised to the positive exponent.
Match Simplified Expression: $(C) 6^{-18}$ does not match our simplified expression because the exponent is $-18$ , which is not the result of $-9 + 2$ .
Match Simplified Expression: $(C) 6^{-18}$ does not match our simplified expression because the exponent is $-18$ , which is not the result of $-9 + 2$ .(D) $\frac{1}{6^{-7}}$ is not equivalent to our simplified expression because it suggests the reciprocal of $6^{-7}$ , which would be $6^7$ .