Select all the expressions that are equivalent to 5^5 * 5^-3. Multi-select Choices: (A)1/5^-15 (B)5^-15 (C)1/5^-2 (D)1/5^2

Use Exponent Properties: To solve this problem, we need to use the properties of exponents. Specifically, when multiplying two powers with the same base, we add the exponents. 5^5 * 5^-3 = 5^(5 + (-3)) = 5^2.Compare with Choices: Now we need to compare the result 5^2 with each of the given choices to determine which are equivalent. (A) 1/5^-15 is not equivalent because the negative exponent indicates the reciprocal, and the base and exponent do not match 5^2.Analysis of Choices: (B) 5^-15 is not equivalent because the exponent -15 does not match the exponent 2 in 5^2.(C) 1/5^-2 is equivalent because the negative exponent indicates the reciprocal, and when we take the reciprocal of 5^-2, we get 5^2.(D) 1/5^2 is equivalent because it is the reciprocal of 5^2, which is the same as 5^2.

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Select all the expressions that are equivalent to $5^5 \times 5^{-3}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{5^{-15}}$ $\newline$ (B) $5^{-15}$ $\newline$ (C) $\frac{1}{5^{-2}}$ $\newline$ (D) $\frac{1}{5^2}$

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Calculus

Find derivatives of using multiple formulae

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Q. Select all the expressions that are equivalent to

5^5 \times 5^{-3}

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{5^{-15}}

\newline

(B)

5^{-15}

\newline

(C)

\frac{1}{5^{-2}}

\newline

(D)

\frac{1}{5^2}

Use Exponent Properties: To solve this problem, we need to use the properties of exponents. Specifically, when multiplying two powers with the same base, we add the exponents. $\newline$ $5^5 \times 5^{-3} = 5^{5 + (-3)} = 5^2$ .
Compare with Choices: Now we need to compare the result $5^2$ with each of the given choices to determine which are equivalent. $\newline$ (A) $\frac{1}{5^{-15}}$ is not equivalent because the negative exponent indicates the reciprocal, and the base and exponent do not match $5^2$ .
Analysis of Choices: $(B) 5^{-15}$ is not equivalent because the exponent $-15$ does not match the exponent $2$ in $5^2$ .
Analysis of Choices: (B) $5^{-15}$ is not equivalent because the exponent $-15$ does not match the exponent $2$ in $5^2$ . (C) $\frac{1}{5^{-2}}$ is equivalent because the negative exponent indicates the reciprocal, and when we take the reciprocal of $5^{-2}$ , we get $5^2$ .
Analysis of Choices: (B) $5^{-15}$ is not equivalent because the exponent $-15$ does not match the exponent $2$ in $5^2$ . (C) $\frac{1}{5^{-2}}$ is equivalent because the negative exponent indicates the reciprocal, and when we take the reciprocal of $5^{-2}$ , we get $5^2$ . (D) $\frac{1}{5^2}$ is equivalent because it is the reciprocal of $5^2$ , which is the same as $5^2$ .