Select all the expressions that are equivalent to 5^5 * 5^5. Multi-select Choices: (A)5^10 (B)1/5^10 (C)1/5^-10 (D)1/5^25

Add Exponents: To solve 5^5 * 5^5, we need to add the exponents since the bases are the same. Calculation: 5^5 * 5^5 = 5^(5+5) = 5^10Calculate Result: Now, let's compare the result with each option: (A) 5^10 matches our result. (B) 1/5^10 is the reciprocal of 5^10, not equivalent. (C) 1/5^-10 is also a reciprocal and represents a large positive power of 5, not equivalent. (D) 1/5^25 is the reciprocal of a much larger power of 5, not equivalent.

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Select all the expressions that are equivalent to $5^5 \times 5^5$ . $\newline$ Multi-select Choices: $\newline$ (A) $5^{10}$ $\newline$ (B) $\frac{1}{5^{10}}$ $\newline$ (C) $\frac{1}{5^{-10}}$ $\newline$ (D) $\frac{1}{5^{25}}$

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Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

5^5 \times 5^5

\newline

Multi-select Choices:

\newline

(A)

5^{10}

\newline

(B)

\frac{1}{5^{10}}

\newline

(C)

\frac{1}{5^{-10}}

\newline

(D)

\frac{1}{5^{25}}

Add Exponents: To solve $5^5 \times 5^5$ , we need to add the exponents since the bases are the same. $\newline$ Calculation: $5^5 \times 5^5 = 5^{5+5} = 5^{10}$
Calculate Result: Now, let's compare the result with each option: $\newline$ (A) $5^{10}$ matches our result. $\newline$ (B) $\frac{1}{5^{10}}$ is the reciprocal of $5^{10}$ , not equivalent. $\newline$ (C) $\frac{1}{5^{-10}}$ is also a reciprocal and represents a large positive power of $5$ , not equivalent. $\newline$ (D) $\frac{1}{5^{25}}$ is the reciprocal of a much larger power of $5$ , not equivalent.