Simplify. Rewrite the expression in the form a^(n). (a^(-13))/(a^(-6))=

Identify base and exponents: Identify the base and the exponents of the numerator and the denominator. In (a^(-13)), a is the base raised to the exponent -13. In (a^(-6)), a is the base raised to the exponent -6. Base: a Exponent of numerator: -13 Exponent of denominator: -6Apply quotient rule for exponents: Apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponents. Rewrite (a^(-13))/(a^(-6)) as a single power of a. (a^(-13))/(a^(-6)) = a^(-13 - (-6)) = a^(-13 + 6) = a^(-7)Check for errors: Check for any mathematical errors in the previous steps. The subtraction of exponents was performed correctly, and the base remains unchanged.Write final simplified expression: Write the final simplified expression. The expression (a^(-13))/(a^(-6)) simplifies to a^(-7).

Home

Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Simplify.

\newline

Rewrite the expression in the form

\newline

a^{n}

\newline

\frac{a^{-13}}{a^{-6}}=

Identify base and exponents: Identify the base and the exponents of the numerator and the denominator. In $(a^{(-13)})$ , $a$ is the base raised to the exponent $-13$ . In $(a^{(-6)})$ , $a$ is the base raised to the exponent $-6$ . $\newline$ Base: $a$ $\newline$ Exponent of numerator: $-13$ $\newline$ Exponent of denominator: $-6$
Apply quotient rule for exponents: Apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponents. Rewrite $(a^{-13})/(a^{-6})$ as a single power of $a$ . $\newline$ $(a^{-13})/(a^{-6}) = a^{-13 - (-6)} = a^{-13 + 6} = a^{-7}$
Check for errors: Check for any mathematical errors in the previous steps. The subtraction of exponents was performed correctly, and the base remains unchanged.
Write final simplified expression: Write the final simplified expression. $\newline$ The expression $(a^{-13})/(a^{-6})$ simplifies to $a^{-7}$ .