Simplify each expression. ( 2 s 3 t ) ( 3 s 4 t 2 ) (2s^3t)(3s^4t^2)

For this problem, we're going to simplify our exponential expression two s cubed times t times three s to the fourth power times t squared, and we're going to do this using our product rule. So first, let's rearrange the terms in this expression so that we can group all of our like factors. So doing this, we're going to first group our constant terms and write two times three. Then we'll group our terms that have a similar base of s, so we'll have times s to the third power and times s to the fourth power, and then our similar terms of t and t squared. Now, let's go ahead and combine our constants and our factors with common bases. So doing that, we have two times three, which makes six, and then s cubed times s to the fourth power. We can use our product rule and combine these by adding the exponents. So we get six times s to the seventh power. And then for t, we have t times t squared. And remember that t by itself is also like saying t to the first power. So to combine these two terms, we're going to add our exponents, and we'll get times t cubed. And this is our exponential expression now in its simplest form.

6. Exponents, Polynomials, and Polynomial Functions

The Product Rule

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

The Product Rule

Struggling with Intermediate Algebra?

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Multiple Choice

Simplify each expression.
$(2 s^{3} t) (3 s^{4} t^{2})$

$6 s to the seventh power t$

$5 s to the seventh power t cubed$

$6s^7t^3$

$5s^3t^7$

Verified step by step guidance

Identify the expression to simplify: $(2s^3t)(3s^4t^2)$.

Multiply the numerical coefficients: multiply 2 and 3 to get \$2 \times 3$.

Apply the product rule for exponents to the variable $s$: add the exponents of $s$ from both terms, which are 3 and 4, so calculate $s^{3+4}$.

Apply the product rule for exponents to the variable $t$: add the exponents of $t$ from both terms, which are 1 and 2, so calculate $t^{1+2}$.

Combine the results from the previous steps to write the simplified expression as the product of the new coefficient and the variables with their new exponents.

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Simplify each expression.(2s3t)(3s4t2)(2s^3t)(3s^4t^2)

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Simplify each expression.
$(2 s^{3} t) (3 s^{4} t^{2})$