Which expressions are equivalent to

\[6\cdot6\cdot6\cdot6\cdot6\] ?
Choose 2 answers:
Choose 2 answers:
(Choice A)
\[(6^2)^3\]
A
\[(6^2)^3\]
(Choice B)
\[2^5\cdot 3^5\]
B
\[2^5\cdot 3^5\]
(Choice C, Checked)

\[\dfrac{6^6}{6^1}\]
C

\[\dfrac{6^6}{6^1}\]
(Choice D)
\[3^2\cdot 2^3\]
D
\[3^2\cdot 2^3\]

1 answer

To find equivalent expressions to \(6 \cdot 6 \cdot 6 \cdot 6 \cdot 6\), we can simplify this expression first:

\[ 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 = 6^5 \]

Now, let's evaluate each choice:

Choice A: \((6^2)^3\)
Using the property of exponents \((a^m)^n = a^{mn}\):

\[ (6^2)^3 = 6^{2 \cdot 3} = 6^6 \]

This expression is not equivalent to \(6^5\).


Choice B: \(2^5 \cdot 3^5\)
We can express \(6\) as \(2 \cdot 3\):

\[ 6^5 = (2 \cdot 3)^5 = 2^5 \cdot 3^5 \]

This expression is equivalent to \(6^5\).


Choice C: \(\frac{6^6}{6^1}\)
Using the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\):

\[ \frac{6^6}{6^1} = 6^{6-1} = 6^5 \]

This expression is equivalent to \(6^5\).


Choice D: \(3^2 \cdot 2^3\)
Calculating this out:

\[ 3^2 \cdot 2^3 = 9 \cdot 8 = 72 \]

And calculating \(6^5\):

\[ 6^5 = 7776 \]

This expression is not equivalent to \(6^5\).


The two correct choices that are equivalent to \(6 \cdot 6 \cdot 6 \cdot 6 \cdot 6\) are:

  • Choice B: \(2^5 \cdot 3^5\)
  • Choice C: \(\frac{6^6}{6^1}\)
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