Simplify the expression using exponent rules . ( − 5 a 2 ) ( 3 a 8 ) \left(-5a^2\right)\left(3a^8\right) ( − 5 a 2 ) ( 3 a 8 )

Welcome back, everyone. Let's try this practice problem here. So here I have negative 5 a squared times 3 a to the 8th power. So whenever you are multiplying numbers and variables, you can multiply numbers with numbers and variables with variables. So, let's go ahead and do that. The 3 and the negative five multiply to 15, and then I have a squared times a to the 8th power. So which of the exponent rules am I gonna use here? I have the same base over here that's multiplied to 2 different exponents, so I can use the product rule. Hopefully, you have your table of rules handy. The product rule means that we can take this a and we can basically just add their exponents together. This is a to the 2 +8 power. And once you're done, you're gonna get negative 15 a to the 10th power. And that is your final answer. Can't simplify this any further, so that's the answer. Thanks for watching.

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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Simplify the expression using exponent rules.
$$\left$(-5a^2$\right$)$\left$(3a^8$\right$)$

$- 8 a^{16}$

$- 10 a^{10}$

$- 15 a^{16}$

$- 15 a^{10}$

Guida verificata passo dopo passo

Identify the expression to simplify: $(-5a^2)(3a^8)$.

Apply the multiplication rule for exponents: When multiplying terms with the same base, add the exponents. Here, the base is $a$, so add the exponents 2 and 8.

Multiply the coefficients: $-5$ and $3$. This gives $-5 \times 3 = -15$.

Combine the results: The coefficient is $-15$ and the exponent for $a$ is $2 + 8 = 10$.

Write the simplified expression: $-15a^{10}$.