Multiplying
What do you do when multiplying powers with the same base?
Ex: (x4)(x8)
You add the powers and keep the base.
Ex: (x4)(x8)=x12
What do you do when you divide powers with the same base?
Ex: x3/x2
You subtract the powers and keep the base.
Ex: x3/x2=x1 or x
What do you do to simplify a power to a power?
Ex: (x5)4
You multiply the exponents (powers).
Ex: (x5)4= x20
What do you do when the exponent is negative?
Ex: x-12
You will move the exponent and its coefficient to the numerator or denominator.
Ex: x-12 is really 1/x12.
How do you simplify an exponent of 0?
Ex: x0
The number simplifies to one. This is because there is no exponent to multiply by, so the number one has to take its place. :>)
Ex: x0=1
Simplify: (w7)(w8)
Answer: w15
Explanation: Since we are multiplying exponents, you have to add the exponents and keep the base. So, w7+8 = w15.
Simplify: d24/d8
Answer: d16
Explanation: When dividing exponents, subtract the exponents and keep the base. d24-8=d16
Simplify: (t4)9
Answer: t36
Explanation: When there's a power to a power, multiply the exponents. 4 x 9 = 36
Simplify: 4-2
Answer: 1/16
Explanation: When there's a negative, move the exponent to the numerator or denominator. After moving 4-2 down to the denominator, the exponent becomes a positive and we must simplify it. 42=16, so our final answer is 1/16. :3
Simplify: (k0)(l3)
Answer is l3.
Explanation: Any number to the power of 0 is equal to 1! k0=1. This leaves l3 as our final answer. 1(l3)=l3.
Simplify: (x13)(x-20)
Answer: 1/x7
Explanation: To get 1/x7, multiply x13 and x-20 by adding their exponents. You will get x-7, but to make it correct, put it under one. :O
Simplify: 3x8/12x5
Answer: x3/4
Explanation: The first step is simplifying 3/12. We will do this by dividing each side by 3, and we will get 1/4. Next, we have to divide x8 and x5 by subtracting their exponents to get x3. When the simplified terms are put together, we should have 1x3/4. The number 1 does not have to be there, so the final answer is x3/4.
Simplify: (a-2)7/a7
Answer: 1/a21
Explanation: When there's a power to a power, multiply the powers. So, (a-2)7= -14. Now we have a-14/a7. When dividing exponents with the same base, keep the base and subtract the exponents. We should get a-21. Since a-21 is a negative exponent in the numerator, we must move it down to the denominator, giving us the answer of 1/a21.
Simplify: (2m2/6 )(m-1/2)
Answer: 2/m1/6
Explanation: First, you multiply the m's by adding the exponents. You have to find a common denominator for m-1/2 in order to add the exponents. The common denominator is 6. So, m-1/2 becomes m-3/6. Then you add m2/6 and m-3/6 to get m-1/6. You bring the 2 down to make it 2m-1/6. To make this proper, move the m-1/6 to the denominator. Finally, the answer is 2/m1/6.
Simplify: a3/a0
Answer: a3
Explanation: The a0 automatically becomes 1, so it would be a3/1. That would simplify to a3. ;P
Simplify: (j4h12)(j-5h6)
Answer: h18/j
Explanation: First, multiply j4 and j-5 by adding their exponents to get j-1. Then, multiply h12 and h6 by adding their exponents to get h18. Finally, bring the j-1 underneath h18.
Simplify: (a2r4)8/a4r
Answer: a12r31
Explanation: First, simplify the power to a power by multiplying the exponents. (a2r4)8=a16r32. Now, divide a16r32/a4r by subtracting their exponents. a16-4r32-1=a12r31! :[
Simplify: (c6/b4)-1/2 (b3/c2)
Answer: b5/c5
Explanation: First, a negative exponent results in the entire fraction flipping and the exponent becoming positive. So, (c6/b4)-1/2=(b4/c6)1/2. Next, simplify the power to a power by multiplying the exponents. (b4/c6)1/2=b2/c3. Now, we have (b5/c5)(b3/c2). Finally, multiply the exponents by adding them. b2+3/c3+2=b5/c5!
Simplify: (-x-7)(2x-9y3)
Answer: -2y3/x16
Explanation: There are two negative exponents in this problem that must move in order to become positive, which are -x-7 and x-9. If we move these, we should rewrite this as, (1/-x7)(2y3/x9). Next, multiply. When multiplying exponents with the same base, keep the base and add the exponents. Our final answer is -2y3/x16!
Simplify: (c12s12)0 (c2s3)
Answer: c2s3
Explanation: When there is a power to a power, multiply the exponents, so (c12s12)0=c0s0. Uh oh! Now there is 0 as an exponent! Well, anything to the power of 0 is equal to 1! c0s0=1! Next, we must multiply, so 1(c2s3)=c2s3. Congrats, this is our final answer!
Simplify: (4a4b8w2)(3a2b-10)
Answer: 12a6w2/b2
Explaination: First, multiply 4 and 3 to get 12. Then, multiply a4 and a2 by keeping the base and adding their exponents to get a6. Next, multiply b8 and b-10 by adding their exponents to get b-2. The w2 will be left alone because there is nothing to multiply it with. So far you should have, 12a6b-2w2. Finally, bring b-2 under the fraction bar. Our final answer is 12a6w2/b2.
Simplify: (s-4/n3)3(7s-10/n6)
Answer:7/n15s22
Explanation: The first step in this problem is to simplify the power to a power by multiplying the exponents. (s-4/n3)3=s-12/n9. We have the negative exponent, s-12, so we must move it to the denominator. 1/n9s12 is the proper form! The next part of this equation, 7s-10/n6 also has a negative exponent. This means that it must be moved to the denominator. After that, we should have (1/n9s12)(7/n6s10). Our next step is multiplying. When we multiply exponents, keep the base and add their exponents. The numerator is 7 because 1x7=7 and the denominator is n15s22 because n9+6s12+10=n15s22. Our final answer is 7/n15s22!
Simplify: (-3n30)2(j4n-12)1/4
Simplify: 9jn57
Explanation: The first step in this problem is to simplify the power to the powers. We do this by multiplying the exponents! (-3n30)2=(-3)2n60, but this can be simplified even further to 9n60! (j4n-12)1/4=jn-3. n-3 must move down to the denominator because a negative as an exponent is not allowed! jn-3=j/n3. Now that we have solved each terms individually, it is time to multiply them. (9n60/1)(j/n3). We multiply exponents with the same base by adding them, so we get 9jn60/n3. The final step is to divide n60 and n3 by subtracting the exponents. 9jn60-3=9jn57, so the final answer is 9jn57! :D
Simplify: (-5-3b2)(1/b-5)(23)
Answer: -8b7/125
Explanation: First, move the negative exponents so then they become positive. When we do this,-5-3b2 becomes b2/-53. We aren't done there though because we can simplify -53 to -125. So, b2/-53=b2/-125. Second, 1/b-5 becomes b5 and that is it. We can simplify 23=8. Now after simplifying each term, we can rewrite the problem as (b2/-125)(b5)(8). Finally, we can multiply! We multiply exponents with the same base by keeping the base and adding the exponents. -8b7/125 is our final answer!
Simplify: (a0l2/3/a7l5)3
Answer: 1/a21l13
Explanation: When there is a power to a power, multiply the exponents. We should have a0l2/a21l15. Next, divide by subtracting the exponents and keeping the base. This should equal l-13/a21. l-13 must be moved down to the denominator because it is a negative exponent and the number one will be our numerator. This gives us 1/a21l13. :D