Select all the expressions that are equivalent to 7^30/7^6. Multi-select Choices: (A)7^24 (B)1/7^5 (C)7^36 (D)1/7^-24

Simplify Expression: Simplify the expression 7^30/7^6 using the properties of exponents. When dividing powers with the same base, we subtract the exponents. 7^30/7^6 = 7^(30 - 6) = 7^24Check Choice (A): Check each answer choice to see if it is equivalent to 7^24. (A) 7^24 is clearly equivalent because it matches the result from Step 1.Check Choice (B): Check choice (B) 1/7^5. 1/7^5 is not equivalent to 7^24 because the exponent is not the same and the expression is a reciprocal, not a product.Check Choice (C): Check choice (C) 7^36. 7^36 is not equivalent to 7^24 because the exponent 36 is not the result of subtracting 6 from 30.Check Choice (D): Check choice (D) 1/7^-24. 1/7^-24 is equivalent to 7^24 because the negative exponent indicates a reciprocal, and taking the reciprocal of a reciprocal gives the original value.

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Select all the expressions that are equivalent to $\frac{7^{30}}{7^6}$ . $\newline$ Multi-select Choices: $\newline$ (A) $7^{24}$ $\newline$ (B) $\frac{1}{7^5}$ $\newline$ (C) $7^{36}$ $\newline$ (D) $\frac{1}{7^{-24}}$

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Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

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Q. Select all the expressions that are equivalent to

\frac{7^{30}}{7^6}

\newline

Multi-select Choices:

\newline

(A)

7^{24}

\newline

(B)

\frac{1}{7^5}

\newline

(C)

7^{36}

\newline

(D)

\frac{1}{7^{-24}}

Simplify Expression: Simplify the expression $7^{30}/7^{6}$ using the properties of exponents. $\newline$ When dividing powers with the same base, we subtract the exponents. $\newline$ $7^{30}/7^{6} = 7^{(30 - 6)} = 7^{24}$
Check Choice (A): Check each answer choice to see if it is equivalent to $7^{24}$ .
(A) $7^{24}$ is clearly equivalent because it matches the result from Step $1$ .
Check Choice (B): Check choice (B) $\frac{1}{7^5}$ . $\frac{1}{7^5}$ is not equivalent to $7^{24}$ because the exponent is not the same and the expression is a reciprocal, not a product.
Check Choice (C): Check choice (C) $7^{36}$ . $7^{36}$ is not equivalent to $7^{24}$ because the exponent $36$ is not the result of subtracting $6$ from $30$ .
Check Choice (D): Check choice (D) $1/7^{-24}$ . $1/7^{-24}$ is equivalent to $7^{24}$ because the negative exponent indicates a reciprocal, and taking the reciprocal of a reciprocal gives the original value.