Simplify each expression. ( x 2 z 5 ) 4 (x^2z^5)^4

this problem, we want to simplify the expression x squared times z to the fifth power all raised to the fourth power. And to do this, we're going to use our power of a product rule by distributing in our fourth power into each of the factors of our product. So we get x squared to the fourth power times z to the fifth power, also to the fourth power. Now using our power rule, we'll multiply our exponents to continue simplifying. So, we have x to the eighth power times z to the twentieth power, and this is our expression now in its simplest form.

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.
$(x^{2} z^{5})^{4}$

$x^6z^9$

$x^{20}z^8$

$x^9z^6$

$x^8z^{20}$

Verified step by step guidance

Recall the Power of a Product Rule, which states that for any numbers $a$ and $b$, and any exponent $n$, the expression $(ab)^n$ can be rewritten as $a^n b^n$.

Identify the base numbers inside the parentheses and the exponent outside the parentheses in the given expression.

Apply the Power of a Product Rule by raising each factor inside the parentheses to the given exponent separately.

Rewrite the expression as the product of each base raised to the exponent, i.e., $a^n \times b^n$.

Simplify each term if possible by calculating powers or combining like terms, but do not calculate the final numeric value unless asked.

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Simplify each expression.(x2z5)4(x^2z^5)^4

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Simplify each expression.
$(x^{2} z^{5})^{4}$