Select all the expressions that are equivalent to 5^5 * 5^9. Multi-select Choices: (A)1/5^14 (B)5^14 (C)5^45 (D)1/5^-14

Apply Exponent Rule: Use the property of exponents that states when multiplying like bases, you add the exponents. So, $5^5 \times 5^9 = 5^{5+9}$. Calculate the sum of the exponents. $5+9 = 14$.Calculate Exponent Sum: Write the result of the exponent addition as a single exponent. $5^5 \times 5^9 = 5^{14}$. Check if this matches any of the given choices.Check Given Choices: Compare the result with the given choices. (A) $1/5^{14}$ is not equivalent because it represents the reciprocal of $5^{14}$. (B) $5^{14}$ is equivalent because it matches the result from Step 2. (C) $5^{45}$ is not equivalent because the exponent is much larger than the result from Step 2. (D) $1/5^{-14}$ is equivalent because it represents the reciprocal of $5^{-14}$, which is $5^{14}$ due to the negative exponent rule.

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Math Problems

Algebra 2

Simplify rational expressions

Full solution

Q. Select all the expressions that are equivalent to

5^5 \times 5^9

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{5^{14}}

\newline

(B)

5^{14}

\newline

(C)

5^{45}

\newline

(D)

\frac{1}{5^{-14}}

Apply Exponent Rule: Use the property of exponents that states when multiplying like bases, you add the exponents. $\newline$ So, $5^5 \times 5^9 = 5^{5+9}$ . $\newline$ Calculate the sum of the exponents. $\newline$ $5+9 = 14$ .
Calculate Exponent Sum: Write the result of the exponent addition as a single exponent. $\newline$ $5^5 \times 5^9 = 5^{14}$ . $\newline$ Check if this matches any of the given choices.
Check Given Choices: Compare the result with the given choices. $\newline$ (A) $1/5^{14}$ is not equivalent because it represents the reciprocal of $5^{14}$ . $\newline$ (B) $5^{14}$ is equivalent because it matches the result from Step $2$ . $\newline$ (C) $5^{45}$ is not equivalent because the exponent is much larger than the result from Step $2$ . $\newline$ (D) $1/5^{-14}$ is equivalent because it represents the reciprocal of $5^{-14}$ , which is $5^{14}$ due to the negative exponent rule.