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Welcome to Brainfuse!

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In this lesson we will work on another rule of exponents

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And that is the Power Rule of Exponents.

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So this rule shows us what happens when an exponent is raised to a power

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On-screen we have x squared raised to the third power, or x squared cubed.

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Let's start with the value inside the parentheses first.

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That's

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x squared. And the exponent, 2, is telling us to multiply x

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Two times.

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And outside of the parentheses, that 3 is telling us to cube the expression. So we need to multiply

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The double x by itself

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3 times.

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To keep it simple we can just copy and paste this term two more times.

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There's x squared to the second power

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And here's x squared to the third power.

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I'll also add in the multiplication signs just so that this is clear

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If we count up

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All of these x's

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This expression is equal to

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2, 4, 6 ... x to the 6th power.

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The power rule of exponents however gives us a shortcut

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We can take to do problems like these, you can just multiply the exponent inside the parentheses

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By the exponent outside of the parentheses.

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As a result that X as a base stays the same and the exponent is equal to 3 x 2.

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That's x to the 6th power.

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This shortcut is helpful here, but it becomes really necessary to use if you have a problem like

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8 to the 4th power

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Raised to the power of 10.

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There's no way that I'm writing that out.

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Right away you'd have to start with 8 x 8 x 8 x 8 and then multiply this expression by itself

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10 times.

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Instead

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You can just multiply the exponents.

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So we keep the base of 8

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And 4 times 10 is equal to 40. So our answer is 8 to the 40th power

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You'll also see algebraic expressions. So let's say we have four cubed

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Raised to the power of y. It would be difficult to write that out because we're not sure what y is.

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But we can simplify it just by multiplying the exponents.

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So three times y is equal to 3y, and our simplified answer will be

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4 raised to the power of 3y. That is 4 cubed multiplied by itself y times.

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Now it's your turn to test out the Power Rule of Exponents. And thank you for watching this lesson!