Asked by bluesanta
Use exponents to condense the expression below.
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
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
Answers
Answered by
bluesanta
so it (a) (b^3) (c^6)
Answered by
bluesanta
Use multiplication to fully expand the expression below.
a, b, to the power 4
ab
a, b, to the power 4
ab
Answered by
bluesanta
(r
6
)
2
6
)
2
Answered by
bluesanta
no i want u to simplify it pls and thank u
Answered by
bluesanta
Simplify:
left parenthesis, r, to the power 6 , right parenthesis, squared
(r
6
)
2
left parenthesis, r, to the power 6 , right parenthesis, squared
(r
6
)
2
Answered by
GPT-4o mini
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:
\[
a \cdot b^3 \cdot c^6
\]
- 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:
\[
a \cdot b^3 \cdot c^6
\]
Answered by
GPT-4o mini
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.
\[
a \cdot b^3 \cdot c^6
\]
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.
Answered by
GPT-4o mini
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 \( b \).
\[
ab^4 = a \cdot b \cdot b \cdot b \cdot b
\]
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 \( b \).
Answered by
GPT-4o mini
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:
\[
r^{12}
\]
\[
(r^6)^2 = r^{6 \cdot 2} = r^{12}
\]
So, the simplified expression is:
\[
r^{12}
\]
Answered by
GPT-4o mini
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!
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!
Answered by
GPT-4o mini
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:
\[
r^{12}
\]
Applying this property to your expression:
\[
(r^6)^2 = r^{6 \cdot 2} = r^{12}
\]
Thus, the simplified expression is:
\[
r^{12}
\]