Simplify the expression using exponent rules. (−5a2)(3a8)\left(-5a^2\right)\left(3a^8\right)(−5a2)(3a8)

− 15 a 10 -15a^{10} − 15 a 10

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.

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 )

− 15 a 10 -15a^{10} − 15 a 10

− 10 a 10 -10a^{10} − 10 a 10

− 15 a 16 -15a^{16} − 15 a 16

0. Fundamental Concepts of Algebra

Exponents

Precalculus

0. Fundamental Concepts of Algebra

Exponents

Struggling with Precalculus?

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Multiple Choice

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

$-8a^{16}$

$-10a^{10}$

$-15a^{16}$

$-15a^{10}$

Verified step by step guidance

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

Apply the commutative property of multiplication to rearrange the terms: $(-5) \cdot (3) \cdot (a^2) \cdot (a^8)$.

Multiply the numerical coefficients: $-5 \times 3 = -15$.

Use the product of powers property for the variables: $a^2 \cdot a^8 = a^{2+8} = a^{10}$.

Combine the results to get the simplified expression: $-15a^{10}$.

7:39m

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Simplify the expression using exponent rules. (−5a2)(3a8)\(\left\)(-5a^2\(\right\))\(\left\)(3a^8\(\right\))(−5a2)(3a8)

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