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

Combine exponents of base: Step 1: Combine the exponents of the same base. 5^-9 * 5^-5 = 5^(-9 + -5) = 5^-14 Convert negative exponent: Step 2: Convert the negative exponent to a positive exponent in the denominator. 5^-14 = 1/5^14 Compare with choices: Step 3: Compare the result with the given choices. 1/5^14 matches choice (B)

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Select all the expressions that are equivalent to $5^{-9} \times 5^{-5}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{5^{45}}$ $\newline$ (B) $\frac{1}{5^{14}}$ $\newline$ (C) $\frac{1}{5^{-14}}$ $\newline$ (D) $5^{-14}$

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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^{-9} \times 5^{-5}

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{5^{45}}

\newline

(B)

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

\newline

(C)

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

\newline

(D)

5^{-14}

Combine exponents of base: Step $1$ : Combine the exponents of the same base. $\newline$ $5^{-9} \times 5^{-5} = 5^{(-9 + -5)} = 5^{-14}$
Convert negative exponent: Step $2$ : Convert the negative exponent to a positive exponent in the denominator. $\newline$ $5^{-14} = \frac{1}{5^{14}}$
Compare with choices: Step $3$ : Compare the result with the given choices. $\newline$ $\frac{1}{5^{14}}$ matches choice (B)