Select all the expressions that are equivalent to 5^-6 * 5^-3. Multi-select Choices: (A)5^-9 (B)1/5^9 (C)5^18 (D)1/5^-9

Use Exponent Properties: To find the equivalent expressions, we need to use the properties of exponents. When multiplying two powers with the same base, we add the exponents. 5^-6 * 5^-3 = 5^(-6 + -3)Add Exponents: Now we perform the addition of the exponents. 5^(-6 + -3) = 5^-9Rewrite Negative Exponent: We can rewrite the negative exponent as a reciprocal to find an equivalent expression. 5^-9 = 1/5^9Check Given Options: Now we check the given options to see which ones match our findings. (A) 5^-9 is equivalent because it is the result of adding the exponents. (B) 1/5^9 is equivalent because it is the reciprocal form of 5^-9. (C) 5^18 is not equivalent because it does not follow the rule of adding exponents for multiplication. (D) 1/5^-9 is not equivalent because it is the reciprocal of the reciprocal of 5^-9, which would give us 5^9, not 5^-9.

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Select all the expressions that are equivalent to $5^{-6} \times 5^{-3}$ . $\newline$ Multi-select Choices: $\newline$ (A) $5^{-9}$ $\newline$ (B) $\frac{1}{5^{9}}$ $\newline$ (C) $5^{18}$ $\newline$ (D) $\frac{1}{5^{-9}}$

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Calculus

Find derivatives of using multiple formulae

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Q. Select all the expressions that are equivalent to

5^{-6} \times 5^{-3}

\newline

Multi-select Choices:

\newline

(A)

5^{-9}

\newline

(B)

\frac{1}{5^{9}}

\newline

(C)

5^{18}

\newline

(D)

\frac{1}{5^{-9}}

Use Exponent Properties: To find the equivalent expressions, we need to use the properties of exponents. When multiplying two powers with the same base, we add the exponents. $\newline$ $5^{-6} \times 5^{-3} = 5^{(-6 + -3)}$
Add Exponents: Now we perform the addition of the exponents. $5^{(-6 + -3)} = 5^{-9}$
Rewrite Negative Exponent: We can rewrite the negative exponent as a reciprocal to find an equivalent expression. $5^{-9} = \frac{1}{5^9}$
Check Given Options: Now we check the given options to see which ones match our findings. $\newline$ (A) $5^{-9}$ is equivalent because it is the result of adding the exponents. $\newline$ (B) $\frac{1}{5^9}$ is equivalent because it is the reciprocal form of $5^{-9}$ . $\newline$ (C) $5^{18}$ is not equivalent because it does not follow the rule of adding exponents for multiplication. $\newline$ (D) $\frac{1}{5^{-9}}$ is not equivalent because it is the reciprocal of the reciprocal of $5^{-9}$ , which would give us $5^9$ , not $5^{-9}$ .