Question Multiply $7x^3$ and $6x^5$ , then select the correct result from the options.

Studdy Solution

STEP 1

Assumptions
1. We are multiplying two monomials: $7x^3$ and $6x^5$ .
2. The exponents in the monomials are to be added when multiplying like bases according to the exponent rules.

STEP 2

To multiply the monomials, we multiply the coefficients (numerical parts) together and then apply the exponent rules for the variables with like bases.
$(Coefficient_1 \times Variable_1^{Exponent_1}) \times (Coefficient_2 \times Variable_2^{Exponent_2})$

STEP 3

Multiply the coefficients $7$ and $6$ .
$7 \times 6 = 42$

STEP 4

Apply the exponent rule for multiplying like bases, which states that when you multiply like bases you add the exponents.
$x^{Exponent_1} \times x^{Exponent_2} = x^{Exponent_1 + Exponent_2}$

STEP 5

Add the exponents $3$ and $5$ .
$3 + 5 = 8$

STEP 6

Combine the results from STEP_3 and STEP_5 to form the final answer.
$42x^8$
The correct answer is $42x^8$ , which corresponds to option d. $42 x^{\wedge} 8$ .

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