Simplify each expression.(−65)5(-6^5)^{^5}

( − 6 ) 25 \left(-6\right)^{25} ( − 6 ) 25

Simplify each expression. ( − 6 5 ) 5 (-6^5)^{^5}

Here we want to simplify the expression negative six to the fifth power all raised to the fifth power. Now, at first, it might not seem like we have a product within these parentheses, but we actually do. We have a negative one multiplied by a six to the fifth power. So to make that easier to see, I'm going to go ahead and rewrite this for you. So we can think of this as the product of negative one times six to the fifth power, all raised to the fifth power. Now we're going to use our power of a product rule and distribute in this five into each of the factors in our product. And we'll get negative one to the fifth power times six to the fifth power raised to the fifth power. Simplifying, we'll evaluate negative one to the fifth power, which is negative one. Since our exponent here is odd, our negative will stay negative. And six to the fifth power raised to the fifth power can be simplified using our power rule by multiplying our exponents. So we'll get negative one times six to the twenty fifth power. And this is now our expression written in its simplest form.

Simplify each expression. ( − 6 5 ) 5 (-6^5)^{^5}

( − 6 ) 25 \left(-6\right)^{25} ( − 6 ) 25

( − 6 ) 10 \left(-6\right)^{10} ( − 6 ) 10

( − 6 ) 5 \left(-6\right)^5 ( − 6 ) 5

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.
$(- 6^{5})^{^{5}}$

$\left(-6\right)^{25}$

$\left(-6\right)^{10}$

$6^{25}$

$\left(-6\right)^5$

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., $a^n b^n$.

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

3:08m

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