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Answer :
To determine which equation correctly shows that
[tex]$$
\left(x^3\right)^2 = x^6,
$$[/tex]
let's use the exponent rules.
1. According to the power of a power rule, if you have [tex]$\left(x^a\right)^b$[/tex], this is equal to [tex]$x^{a \cdot b}$[/tex]. Thus,
[tex]$$
\left(x^3\right)^2 = x^{3 \cdot 2} = x^6.
$$[/tex]
2. Another way to see this is by writing
[tex]$$
\left(x^3\right)^2 = x^3 \cdot x^3.
$$[/tex]
When multiplying with the same base, you add the exponents:
[tex]$$
x^3 \cdot x^3 = x^{3+3} = x^6.
$$[/tex]
3. Option B shows these steps by expressing [tex]$\left(x^3\right)^2$[/tex] as [tex]$x^3 \cdot x^3$[/tex], which then results in [tex]$x^6$[/tex] when written out as [tex]$x\cdot x\cdot x\cdot x\cdot x\cdot x$[/tex].
Thus, the equation in Option B correctly demonstrates that
[tex]$$
\left(x^3\right)^2 = x^6.
$$[/tex]
The correct answer is Option B.
[tex]$$
\left(x^3\right)^2 = x^6,
$$[/tex]
let's use the exponent rules.
1. According to the power of a power rule, if you have [tex]$\left(x^a\right)^b$[/tex], this is equal to [tex]$x^{a \cdot b}$[/tex]. Thus,
[tex]$$
\left(x^3\right)^2 = x^{3 \cdot 2} = x^6.
$$[/tex]
2. Another way to see this is by writing
[tex]$$
\left(x^3\right)^2 = x^3 \cdot x^3.
$$[/tex]
When multiplying with the same base, you add the exponents:
[tex]$$
x^3 \cdot x^3 = x^{3+3} = x^6.
$$[/tex]
3. Option B shows these steps by expressing [tex]$\left(x^3\right)^2$[/tex] as [tex]$x^3 \cdot x^3$[/tex], which then results in [tex]$x^6$[/tex] when written out as [tex]$x\cdot x\cdot x\cdot x\cdot x\cdot x$[/tex].
Thus, the equation in Option B correctly demonstrates that
[tex]$$
\left(x^3\right)^2 = x^6.
$$[/tex]
The correct answer is Option B.
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