Please help!
(a^2)63
(-2x)^3
(p^2q)^3
-5c(2cd)^3
4y(y62z)63
(12a^5)^2b^3
6a(-ab)^7
(-2d^2)^6(-3)^3
please and thanc u!
Learn and apply these rules for taking powers of numbers with exponents,
(x^a)^b = x^(ab) ,
(x^a*y^b)^c = x^(ac) * y^(bc)
and multiplying variables with exponents.
x^a*x^b = x^(a+b)
Here is how this works with two examples. You should do the rest yourself.
(p^2*q)^3 = p^6*q^3
6a(-ab)^7 = 6a*(-1)^7 * a^7 * b^7
= -6a^8 * b^7
The * symbol indicates multiplication, but could be left out
Sure! I can help you simplify these expressions. To do that, we'll use the exponent rules. Let's go through each expression one by one:
1. (a^2)^63:
To simplify this expression, we multiply the exponents inside the parentheses with the exponent outside. So, (a^2)^63 becomes a^(2*63), which simplifies to a^126.
2. (-2x)^3:
To simplify this expression, we apply the exponent to each term inside the parentheses. So, (-2x)^3 becomes (-2)^3 * x^3, which simplifies to -8x^3.
3. (p^2q)^3:
To simplify this expression, we apply the exponent to each term inside the parentheses. So, (p^2q)^3 becomes (p^2)^3 * q^3. Applying the exponent to p^2, we get p^(2*3) * q^3, which simplifies to p^6q^3.
4. -5c(2cd)^3:
To simplify this expression, we first evaluate the exponent of (2cd)^3 which becomes 2^3 * c^3 * d^3. Then, we multiply this result by -5c. So, -5c(2cd)^3 simplifies to -5c * 2^3 * c^3 * d^3, which can be further simplified to -40c^4d^3.
5. 4y(y^62z)^63:
To simplify this expression, we first evaluate the exponent of (y^62z)^63 which becomes y^(62*63) * z^(63). Then, we multiply this result by 4y. So, 4y(y^62z)^63 simplifies to 4y * y^(62*63) * z^(63), which can be further simplified to 4y^(3906)z^(63).
6. (12a^5)^2b^3:
To simplify this expression, we first apply the exponent to (12a^5)^2 which becomes 12^2 * (a^5)^2 * b^3. Then, we simplify each term inside the parentheses. 12^2 equals 144, (a^5)^2 simplifies to a^(5*2) which is a^10. Thus, (12a^5)^2b^3 simplifies to 144a^10b^3.
7. 6a(-ab)^7:
To simplify this expression, we first evaluate the exponent of (-ab)^7 which becomes -a^7 * b^7. Then, we multiply this result by 6a. So, 6a(-ab)^7 simplifies to 6a * -a^7 * b^7, which can be further simplified to -6a^8b^7.
8. (-2d^2)^6(-3)^3:
To simplify this expression, we first solve the exponent of (-2d^2)^6 which becomes (-2)^6 * (d^2)^6. Then, we simplify each term inside the parentheses. (-2)^6 equals 64, and (d^2)^6 simplifies to d^(2*6) which is d^12. Finally, we multiply this result by (-3)^3 which equals -3^3. So, (-2d^2)^6(-3)^3 simplifies to 64d^12 * -27.
I hope this helps! Let me know if there's anything else I can assist you with.