Question - Multiplying Powers with Coefficients
Solution:
First, multiply the coefficients: \( 12 \times 8 \times \frac{3}{4} = 24 \times 3 = 72 \)
Next, add the exponents of \( p \): \( 6 + 3 + 7 = 16 \)
The final answer is \( 72p^{16} \)
Tutor Solution:
Let's solve the expression \(12p^6 \times 8p^3 \times \frac{3}{4}p^7\) step by step.
1. **Multiply the coefficients (numerical parts)**: First, we have the coefficients \(12\), \(8\), and \(\frac{3}{4}\). We will multiply these together:
\[ 12 \times 8 = 96 \] Then, multiply \(96\) by \(\frac{3}{4}\): \[ 96 \times \frac{3}{4} = \frac{96 \times 3}{4} = \frac{288}{4} = 72 \]So the final coefficient is \(72\).
2. **Combine the powers of \(p\)**: Next, we will combine the powers of \(p\) present in the expression:
\[ p^6 \times p^3 \times p^7 \] When multiplying powers that have the same base, we add the exponents: \[ p^{6 + 3 + 7} = p^{16} \]3. **Combine the results**: Now, we combine the final coefficient with the power of \(p\) that we calculated:
\[ 72p^{16} \]Thus, the final answer is \(72p^{16}\).
In summary, we found the product of the coefficients and combined the powers of \(p\) to arrive at the solution. If you look at the options given, this corresponds to option \(A\) (assuming it says \(72p^{16}\)).
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