(a^(8)b^(-2))/(a^(2)b^(10)) Which of the following is equivalent to the given expression for a,b!=0 ? Choose 1 answer: (A) a^(4)b^(-5) (B) a^(6)b^(12) (C) (a^(4))/(b^(-5)) (D) (a^(6))/(b^(12))

Given expression: We are given the expression $(a^{8}b^{-2})/(a^{2}b^{10})$. To simplify this expression, we use the properties of exponents, specifically the quotient rule which states that when dividing like bases, we subtract the exponents: $a^{m}/a^{n} = a^{m-n}$ and $b^{m}/b^{n} = b^{m-n}$.Applying quotient rule: Applying the quotient rule to the given expression, we get: $a^{8-2}b^{-2-10} = a^{6}b^{-12}$.Simplified expression: The simplified expression $a^{6}b^{-12}$ can be rewritten as $(a^{6})/(b^{12})$ because $b^{-12} = 1/b^{12}$.Comparing with answer choices: Now we compare our simplified expression with the answer choices. The expression $(a^{6})/(b^{12})$ matches with choice (D).

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(a^(8)b^(-2))/(a^(2)b^(10))
Which of the following is equivalent to the given expression for
a,b!=0 ?
Choose 1 answer:
(A)
a^(4)b^(-5)
(B)
a^(6)b^(12)
(C)
(a^(4))/(b^(-5))
(D)
(a^(6))/(b^(12))

$\frac{a^{8} b^{-2}}{a^{2} b^{10}}$ $\newline$ Which of the following is equivalent to the given expression for $a, b \neq 0$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $a^{4} b^{-5}$ $\newline$ (B) $a^{6} b^{12}$ $\newline$ (C) $\frac{a^{4}}{b^{-5}}$ $\newline$ (D) $\frac{a^{6}}{b^{12}}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\frac{a^{8} b^{-2}}{a^{2} b^{10}}

\newline

Which of the following is equivalent to the given expression for

a, b \neq 0

\newline

Choose

1

answer:

\newline

(A)

a^{4} b^{-5}

\newline

(B)

a^{6} b^{12}

\newline

(C)

\frac{a^{4}}{b^{-5}}

\newline

(D)

\frac{a^{6}}{b^{12}}

Given expression: We are given the expression $(a^{8}b^{-2})/(a^{2}b^{10})$ . To simplify this expression, we use the properties of exponents, specifically the quotient rule which states that when dividing like bases, we subtract the exponents: $a^{m}/a^{n} = a^{m-n}$ and $b^{m}/b^{n} = b^{m-n}$ .
Applying quotient rule: Applying the quotient rule to the given expression, we get: $\newline$ $a^{8-2}b^{-2-10} = a^{6}b^{-12}$ .
Simplified expression: The simplified expression $a^{6}b^{-12}$ can be rewritten as $(a^{6})/(b^{12})$ because $b^{-12} = 1/b^{12}$ .
Comparing with answer choices: Now we compare our simplified expression with the answer choices. The expression $(a^{6})/(b^{12})$ matches with choice (D).