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 and Polynomials

Intro to the Power Rules

Beginning Algebra

6. Exponents and Polynomials

Intro to the Power Rules

Struggling with Beginning Algebra?

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Multiple Choice

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

$x^{\frac89}$

$x^{-1}$

$x^1$

$x^{\frac12}$

Verified step by step guidance

Identify the expression or terms that involve exponents in the problem. The Power Rule for Exponents states that when you raise a power to another power, you multiply the exponents.

Write down the Power Rule formula: $ (a^{m})^{n} = a^{m \times n} $. This means if you have a base $a$ raised to an exponent $m$, and then the whole expression is raised to another exponent $n$, you multiply $m$ and $n$.

Apply the Power Rule to the given expression by multiplying the exponents. For example, if the problem has $ (x^{3})^{4} $, rewrite it as $ x^{3 \times 4} $.

Simplify the multiplication of the exponents to get the new exponent. In the example, $ 3 \times 4 = 12 $, so the expression becomes $ x^{12} $.

If there are multiple terms with exponents, apply the Power Rule to each term separately, and then simplify the expression as needed.

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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.
$\frac{(x^{2})^{4}}{{(x^{3})}^{3}}$