Simplify each expression, but don’t evaluate. ( x 2 ) 4 ( x 3 ) 3 \frac{(x^2)^4}{\left(x^3\right)^3}

this problem, we want to simplify the expression x squared to the fourth power divided by x cubed to the third power. And to do this, we're going to use a couple of the rules we've learned so far. First, let's apply the power rule to simplify our exponents raised to other exponents. And we know that to do so, we simply multiply the exponents. So our first step is to multiply two times four to get our numerator as x to the eighth power, and that's going to be divided by x to the three times three power, so x to the ninth power. Now we can use our quotient rule because we have a exponential expression being divided by another exponential expression, expression, and they both have the same base value of x. So our quotient rule tells us that we need to subtract our exponents. So, we'll get x to the eight minuteus nine power, so x to the negative one power.

6. Exponents, Polynomials, and Polynomial Functions

Intro to the Power Rules

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Intro to the Power Rules

Struggling with Intermediate Algebra?

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Multiple Choice

Simplify each expression, but don’t evaluate.
$\frac{(x^{2})^{4}}{{(x^{3})}^{3}}$

$x^{\frac{8}{9}}$

$x^{- 1}$

$x^1$

$x^{\frac12}$

Verified step by step guidance

Identify the expression to simplify: $\frac{(x^2)^4}{(x^3)^3}$.

Apply the power of a power rule, which states that $(a^m)^n = a^{m \times n}$, to both the numerator and the denominator. This gives $x^{2 \times 4}$ in the numerator and $x^{3 \times 3}$ in the denominator.

Rewrite the expression using the simplified exponents: $\frac{x^8}{x^9}$.

Use the quotient rule for exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$, to combine the terms: $x^{8 - 9}$.

Express the final simplified form as $x^{-1}$, which indicates the variable $x$ raised to the power of negative one.

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Simplify each expression, but don’t evaluate.(x2)4(x3)3\frac{(x^2)^4}{\left(x^3\right)^3}

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Simplify each expression, but don’t evaluate.
$\frac{(x^{2})^{4}}{{(x^{3})}^{3}}$