Question

6(h^7)^4, -2(y^5)^6, -(d^3)^5, ((2)^4)^2, ((-3)^2)^2, ((-5)^2)^2

Answer 1

$6 {h}^{28} \\ - 2 {y}^{30} \\ - {d}^{15} \\ {2}^{8} = 256 \\ {( - 3)}^{4} = 81 \\ {( - 5)}^{4} = 625$

Answer 2

To simplify each expression, you need to apply the rule of exponents, which states that when you raise a power to another power, you multiply the exponents. Let's simplify each expression step by step:

1. 6(h^7)^4: Apply the exponent rule: (a^b)^c = a^(b * c) 6(h^7)^4 = 6 * h^(7 * 4) = 6h^28

2. -2(y^5)^6: Apply the exponent rule: (a^b)^c = a^(b * c) -2(y^5)^6 = -2 * y^(5 * 6) = -2y^30

3. -(d^3)^5: Apply the exponent rule: (a^b)^c = a^(b * c) -(d^3)^5 = -(d^(3 * 5)) = -(d^15)

4. ((2)^4)^2: Apply the exponent rule: (a^b)^c = a^(b * c) ((2)^4)^2 = (2^(4 * 2)) = 2^8 = 256

5. ((-3)^2)^2: Apply the exponent rule: (a^b)^c = a^(b * c) ((-3)^2)^2 = ((-3)^(2 * 2)) = (-3)^4 = 81

6. ((-5)^2)^2: Apply the exponent rule: (a^b)^c = a^(b * c) ((-5)^2)^2 = ((-5)^(2 * 2)) = (-5)^4 = 625

So, the simplified expressions are:

1. 6(h^7)^4 = 6h^28
2. -2(y^5)^6 = -2y^30
3. -(d^3)^5 = -(d^15)
4. ((2)^4)^2 = 256
5. ((-3)^2)^2 = 81
6. ((-5)^2)^2 = 625