Math  /  Algebra

QuestionSolve: (2x3)(6x4)\left(2 x^{3}\right)\left(6 x^{4}\right) 8x78 x^{7} 8x128 x^{12} 12x712 x^{7} 12x1212 x^{12}

Studdy Solution

STEP 1

What is this asking? Simplify the expression (2x3)(6x4)\left(2 x^{3}\right)\left(6 x^{4}\right) and find which of the given options matches the result. Watch out! Don't forget to multiply both the coefficients and the exponents separately!

STEP 2

1. Multiply the coefficients
2. Add the exponents

STEP 3

Alright, let's start by focusing on the numbers in front of the xx's.
We have 22 and 66.
When we multiply these together, we get:
26=122 \cdot 6 = 12This gives us the coefficient for our simplified expression.
Easy peasy!

STEP 4

Now, let's deal with the exponents.
We've got x3x^{3} and x4x^{4}.
When multiplying like bases, we **add the exponents**.
So, we do:
3+4=73 + 4 = 7This means the exponent for xx in our simplified expression is 77.

STEP 5

Putting it all together, the simplified expression is:
12x712 x^{7}So, the correct answer is 12x712 x^{7}!

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