(a^(m))^(n)*a^(mn) Which of the following is equivalent to the given expression? Choose 1 answer: (A) 2a^(mn) (B) a^(2mn) (C) a^(m^(2)n^(2)) (D) a^(m^(n)+mn)

Apply Power Rule: Use the power of a power rule, which states that (a^m)^n = a^(m*n). (a^(m))^n = a^(m*n)Use Product Rule: Now, multiply the result by a^(mn) using the product of powers rule, which states that a^b * a^c = a^(b+c). a^(m*n) * a^(mn) = a^(m*n + mn)Factor out Common Factor: Simplify the exponent by factoring out the common factor m. a^(m*n + mn) = a^(m(n + n))Simplify Exponent: Since n + n = 2n, the expression simplifies further. a^(m(n + n)) = a^(m*2n)Further Simplification: Finally, we have the simplified expression. a^(m*2n) = a^(2mn)

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(a^(m))^(n)*a^(mn)
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
2a^(mn)
(B)
a^(2mn)
(C)
a^(m^(2)n^(2))
(D)
a^(m^(n)+mn)

$\left(a^{m}\right)^{n} \cdot a^{m n}$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $2 a^{m n}$ $\newline$ (B) $a^{2 m n}$ $\newline$ (C) $a^{m^{2} n^{2}}$ $\newline$ (D) $a^{m^{n}+m n}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\left(a^{m}\right)^{n} \cdot a^{m n}

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

2 a^{m n}

\newline

(B)

a^{2 m n}

\newline

(C)

a^{m^{2} n^{2}}

\newline

(D)

a^{m^{n}+m n}

Apply Power Rule: Use the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . $\newline$ $(a^{(m)})^n = a^{m*n}$
Use Product Rule: Now, multiply the result by $a^{mn}$ using the product of powers rule, which states that $a^b \cdot a^c = a^{b+c}$ . $\newline$ $a^{m\cdot n} \cdot a^{mn} = a^{m\cdot n + mn}$
Factor out Common Factor: Simplify the exponent by factoring out the common factor $m$ . $a^{m*n + mn} = a^{m(n + n)}$
Simplify Exponent: Since $n + n = 2n$ , the expression simplifies further. $\newline$ $a^{m(n + n)} = a^{m\cdot 2n}$
Further Simplification: Finally, we have the simplified expression. $a^{(m*2n)} = a^{2mn}$