Question
\( \mid \leftarrow \quad \) Simplify the exponential expression. \[ \left(5 x^{9}\right)\left(5 x^{2}\right) \] \( \left(5 x^{9}\right)\left(5 x^{2}\right)=\square \)
Ask by Mckenzie Pollard. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\left(5 x^{9}\right)\left(5 x^{2}\right) = 25 x^{11}
\]
Solution
To simplify the exponential expression:
\[
\left(5 x^{9}\right)\left(5 x^{2}\right)
\]
**Step 1: Multiply the coefficients.**
\[
5 \times 5 = 25
\]
**Step 2: Multiply the variables by adding their exponents.**
\[
x^{9} \times x^{2} = x^{9+2} = x^{11}
\]
**Combine the results:**
\[
\left(5 x^{9}\right)\left(5 x^{2}\right) = 25 x^{11}
\]
\[
\left(5 x^{9}\right)\left(5 x^{2}\right) = 25 x^{11}
\]
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Simplify this solution The Deep Dive
To simplify the expression \( \left(5 x^{9}\right)\left(5 x^{2}\right) \), we start by multiplying the coefficients and then applying the properties of exponents. The coefficients \( 5 \) and \( 5 \) multiply to \( 25 \). For the variables, we add the exponents since the bases are the same: \( x^{9} \cdot x^{2} = x^{9+2} = x^{11} \). So, the simplified expression is: \[ \left(5 x^{9}\right)\left(5 x^{2}\right) = 25 x^{11} \]
