Simplify each expression.(4x3y2z3)2(4x^3y^2z^3)^2

16 x 6 y 4 z 6 16x^6y^4z^6 16 x 6 y 4 z 6

Simplify each expression. ( 4 x 3 y 2 z 3 ) 2 (4x^3y^2z^3)^2

this problem, we're going to simplify the expression four times x cubed times y squared times z cubed all squared, and we'll do this using our power of a product rule by distributing in our squared exponent into each of the factors in our product. So doing that, we'll end up with four squared times x cubed squared times y squared squared times z cubed squared. Continuing to simplify, we can evaluate four squared as 16. X cubed all squared becomes x to the sixth power by multiplying our exponents. Same thing here, multiplying our exponents, we'll get y to the fourth power. And for our final term, we'll multiply our exponents to get z to the sixth power. And this is our expression, now in its simplest form.

Simplify each expression. ( 4 x 3 y 2 z 3 ) 2 (4x^3y^2z^3)^2

16 x 6 y 4 z 6 16x^6y^4z^6 16 x 6 y 4 z 6

16 x 3 y 2 z 3 16x^3y^2z^3 16 x 3 y 2 z 3

4 x 3 y 4 z 6 4x^3y^4z^6 4 x 3 y 4 z 6

6. Exponents, Polynomials, and Polynomial Functions

Intro to the Power Rules

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Intro to the Power Rules

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Multiple Choice

Simplify each expression.
$open paren 4 x cubed y squared z cubed close paren squared$

$8 x^{6} y^{4} z^{6}$

$16x^6y^4z^6$

$16x^3y^2z^3$

$4x^3y^4z^6$

Verified step by step guidance

Identify the expression to simplify: $\left(4x^{3}y^{2}z^{3}\right)^{2}$.

Apply the power of a product rule, which states that $\left(abc\right)^n = a^n b^n c^n$. So, raise each factor inside the parentheses to the power of 2: \$4^{2}$, $\left(x^{3}\right)^{2}$, $\left(y^{2}\right)^{2}$, and $\left(z^{3}\right)^{2}$.

Use the power of a power rule for the variables: $\left(x^{m}\right)^{n} = x^{m \times n}$. Calculate the new exponents: $x^{3 \times 2}$, $y^{2 \times 2}$, and $z^{3 \times 2}$.

Calculate the numerical coefficient by squaring 4: \$4^{2}$.

Combine the results to write the simplified expression as \$4^{2} x^{6} y^{4} z^{6}$.

3:08m

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