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Answer :
To simplify the expression [tex]\(9x(5x^2)\)[/tex], follow these steps:
1. Identify the Components: The expression consists of multiplying a number with a variable, which is [tex]\(9x\)[/tex], by another term, [tex]\(5x^2\)[/tex].
2. Multiply the Coefficients: Multiply the numbers (coefficients) together:
[tex]\[
9 \times 5 = 45
\][/tex]
3. Add the Exponents of the Like Base: When multiplying expressions with the same base, add the exponents:
[tex]\[
x \times x^2 = x^{1+2} = x^3
\][/tex]
4. Combine the Results: Put the coefficient and the variable parts together:
[tex]\[
45x^3
\][/tex]
So, the simplified expression is [tex]\(45x^3\)[/tex], which matches option D.
1. Identify the Components: The expression consists of multiplying a number with a variable, which is [tex]\(9x\)[/tex], by another term, [tex]\(5x^2\)[/tex].
2. Multiply the Coefficients: Multiply the numbers (coefficients) together:
[tex]\[
9 \times 5 = 45
\][/tex]
3. Add the Exponents of the Like Base: When multiplying expressions with the same base, add the exponents:
[tex]\[
x \times x^2 = x^{1+2} = x^3
\][/tex]
4. Combine the Results: Put the coefficient and the variable parts together:
[tex]\[
45x^3
\][/tex]
So, the simplified expression is [tex]\(45x^3\)[/tex], which matches option D.
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