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. Functions

Exponent Rules

Business Calculus

0. Functions

Exponent Rules

Struggling with Business Calculus?

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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

Step 1: Start by simplifying the first part of the expression $(-5a^2)(3a^8)$. Use the distributive property of multiplication and the product rule of exponents, which states that $a^m \cdot a^n = a^{m+n}$.

Step 2: Multiply the coefficients $-5$ and $3$ to get $-15$. Then, add the exponents of $a$: $2 + 8 = 10$. This simplifies the first part to $-15a^{10}$.

Step 3: Now compare the simplified expression $-15a^{10}$ with the given options. The correct answer should match this simplified form.

Step 4: Verify that the correct answer is $-15a^{10}$, as it matches the simplified expression obtained in Step 2.

Step 5: Conclude that the correct answer is $-15a^{10}$, as it satisfies the rules of exponentiation and multiplication.

7:39m

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