Use exponents to condense the expression below.

Question

a, dot, b, dot, b, dot, b, dot, c, dot, c, dot, c, dot, c, dot, c, dot, c
a⋅b⋅b⋅b⋅c⋅c⋅c⋅c⋅c⋅c

Answer 1

To condense the expression \( a \cdot b \cdot b \cdot b \cdot c \cdot c \cdot c \cdot c \cdot c \cdot c \) using exponents, we can count how many times each variable appears:

• The variable \( a \) appears 1 time.
• The variable \( b \) appears 3 times.
• The variable \( c \) appears 6 times.

Therefore, we can express the condensed form using exponents as follows:

\[ a^1 \cdot b^3 \cdot c^6 \]

Since \( a^1 \) can be simply written as \( a \), the final condensed expression is:

\[ a \cdot b^3 \cdot c^6 \]

Answer 2

so it (a) (b^3) (c^6)

Answer 3

Yes, that's correct! The condensed expression can be written as:

\[ a \cdot b^3 \cdot c^6 \]

Alternatively, if you prefer to use parentheses, you could write it as:

\[ (a)(b^3)(c^6) \]

Both notations are valid and represent the same mathematical expression.

Answer 4

Use multiplication to fully expand the expression below.
a, b, to the power 4
ab

Answer 5

To fully expand the expression \( ab^4 \) using multiplication, we express it as follows:

\[ ab^4 = a \cdot b \cdot b \cdot b \cdot b \]

So, the fully expanded expression is:

\[ a \cdot b \cdot b \cdot b \cdot b \]

You can also write this without the multiplication symbols for clarity:

\[ abbbb \]

Thus, \( ab^4 \) expands to \( a \) followed by four instances of \( b \).

Answer 6

(r
6
)
2

Answer 7

The expression you provided seems to be \( (r^6)^2 \). To simplify this using the power of a power property of exponents, you multiply the exponents together:

\[ (r^6)^2 = r^{6 \cdot 2} = r^{12} \]

So, the simplified expression is:

\[ r^{12} \]

Answer 8

no i want u to simplify it pls and thank u

Answer 9

I apologize for any misunderstanding earlier. Let's clarify the expression properly.

If you are referring to \( \binom{r}{6}^2 \), which denotes the square of the binomial coefficient "r choose 6", then:

\[ \left( \binom{r}{6} \right)^2 \]

This does not simplify further unless \( r \) is specified. The binomial coefficient \( \binom{r}{k} \) is defined as:

\[ \binom{r}{6} = \frac{r!}{6!(r-6)!} \]

So, squaring it would give:

\[ \left( \binom{r}{6} \right)^2 = \left( \frac{r!}{6!(r-6)!} \right)^2 = \frac{(r!)^2}{(6!)^2((r-6)!)^2} \]

If you meant something else by \( (r 6)^2 \) or any further simplifications, please clarify, and I would be happy to assist you! Thank you!

Answer 10

Simplify:
left parenthesis, r, to the power 6 , right parenthesis, squared
(r
6
)
2

Answer 11

It looks like you're asking to simplify the expression \( (r^6)^2 \). To simplify this expression, we can use the power of a power property of exponents, which states that \( (a^m)^n = a^{m \cdot n} \).

Applying this property to your expression:

\[ (r^6)^2 = r^{6 \cdot 2} = r^{12} \]

Thus, the simplified expression is:

\[ r^{12} \]