Answer :
To solve the expression [tex]\( \left(x^6\right) \cdot\left(x^2\right) \)[/tex], we need to use the properties of exponents. When we multiply two powers that have the same base, we add their exponents. Let's break this down step-by-step:
1. Identify the base and the exponents: The base here is [tex]\( x \)[/tex], and the exponents are 6 and 2.
2. Apply the property of exponents: When multiplying [tex]\( x^a \)[/tex] by [tex]\( x^b \)[/tex], we add the exponents [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
So, [tex]\( \left(x^6\right) \cdot\left(x^2\right) \)[/tex] can be rewritten as:
[tex]\[ x^{6+2} \][/tex]
3. Calculate the sum of the exponents: Add 6 and 2 together.
[tex]\[ 6 + 2 = 8 \][/tex]
Therefore, the expression [tex]\( \left(x^6\right) \cdot\left(x^2\right) \)[/tex] simplifies to [tex]\( x^8 \)[/tex].
Thus, the correct choice is:
[tex]\[ x^8 \][/tex]
1. Identify the base and the exponents: The base here is [tex]\( x \)[/tex], and the exponents are 6 and 2.
2. Apply the property of exponents: When multiplying [tex]\( x^a \)[/tex] by [tex]\( x^b \)[/tex], we add the exponents [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
So, [tex]\( \left(x^6\right) \cdot\left(x^2\right) \)[/tex] can be rewritten as:
[tex]\[ x^{6+2} \][/tex]
3. Calculate the sum of the exponents: Add 6 and 2 together.
[tex]\[ 6 + 2 = 8 \][/tex]
Therefore, the expression [tex]\( \left(x^6\right) \cdot\left(x^2\right) \)[/tex] simplifies to [tex]\( x^8 \)[/tex].
Thus, the correct choice is:
[tex]\[ x^8 \][/tex]
