/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 Simplify. \((3 r)^{2}\left(6 r... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 6

Simplify. \((3 r)^{2}\left(6 r^{8}\right)^{2}\)

Short Answer

Expert verified
The simplified expression is \(324r^{18}\).

Step by step solution

01

Apply the exponent rule (ab)^n = a^n b^n #

Using the exponent rule, we can expand the given expression: \[(3r)^2(6r^8)^2 = (3^2r^2)(6^2(r^8)^2).\]
02

Apply the exponent rule (a^m)^n = a^{mn} #

Applying the exponent rule to simplify the term with the exponent of two exponentials, we get: \[(3^2r^2)(6^2(r^8)^2) = (3^2r^2)(6^2r^{8 \times 2}).\]
03

Combine terms with the same base #

We can combine the terms with the same base (r) by adding their exponents: \[(3^2r^2)(6^2r^{8 \times 2}) = (3^2 \times 6^2)r^{2+8 \times 2}.\]
04

Simplify constant terms #

Simplifying the constant terms by multiplying them together, we get: \[(3^2 \times 6^2)r^{2+8 \times 2} = 9 \times 36 r^{2+16} = 324r^{18}.\] So, the simplified expression is \(324r^{18}\).

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