Math chapter 3 exponential expressions to powers
- 2. How do we simplify (52)3 ? Expand: (5. 5)3 Expand further: (5. 5). (5. 5). (5. 5) Evaluate: 5. 5. 5. 5. 5. 5 = 56 (52)3 = 52 . 3 = 56
- 3. How do we simplify (yx3)3 ? Expand: ( y . x . x . x) . (y . x . x . x) . (y . x . x . x) = y . x . x . x . y . x . x . x . y . x . x . x Rearrange: = x . x . x . x . x . x . x . x . x . y . y . y = x9y3
- 4. Let’s try (x10)3 Expand: x10. x10. x10 = x30
- 5. The Rule: When we see an exponential expression raised to a power such as (x2)3, this means that we have three groups of x2 to multiply. We will have 3 groups of 2 x’s multiplied together, and this gives us a total of 6. So (x2)3 = x6. This is always true no matter what we have in our parentheses; if we have all multiplication, we will have that many groups of each.
- 6. The Rule: When we see something like (5x3y7)5, we will have five 5’s, five x3 – so five groups of 3 x’s multiplied together, and five groups of seven y’s multiplied together. In total, we will have five 5’s, 15 x’s, and 35 y’s. This means that (5x3y7)5 = 55 x15 y35 or 3125x15y35.”
Editor's Notes
- #3: Let’s simplify (52)3. What does this mean? Let’s write this out in expanded form. We have two exponents, though. What should we do first? Let’s do what is in the parentheses first. Now what does this exponent of 3 mean to do? It means we write the entire amount in the parentheses 3 times. But this is all multiplication. So we see that we have six 5’s multiplies together. We can write this as 56. So (52)3 = 56.
- #4: “Now we see that once again we have all multiplication. But we do not have all the same variable. Since multiplication is commutative, we can rewrite this so we have similar variables grouped together.”
- #5: Now if we write out what is in the parentheses first, this will be very long. But we could think of this as x10. x10. x10. Now we could continue to write all these out, but we already know how to multiply with the same bases. This would be x30.