Simplify the expression (- 5g ^ 5 * h ^ 6) ^ 2 * (g ^ 4 * h ^ 2) ^ 4 A (g ^ 26 * h ^ 20)/25 B 25s ^ 26 * h ^ 20 25g ^ 15 * h ^ 14 D - 25g ^ 26 * h ^ 20

Answer 1

(-5g^5*h^6)^2=(-5gh^11)^2=-5gh^22.........................

Answer 2

Note: I'm going to assume that the "s" in the B option was supposed to be a "g" because that is the only logical answer.

Question: (-5g⁵ * h⁶)² * (g⁴ * h²)⁴

A. (g²⁶ * h²⁰) / 25

B. 25g²⁶ * h²⁰

C. 25g¹⁵ * h¹⁴

D. -25g²⁶ * h²⁰

(-5g⁵ * h⁶)² * (g⁴ * h²)⁴

1. The first thing to understand is that the exponents inside of the parentheses need to be multiplied by the exponent outside of the parentheses. Additionally, according to the exponent rule, (-a)ⁿ = aⁿ. Taking the first half of the expression, a simplification would look like this:

(-5g⁵ * h⁶)²

(5g⁵h⁶)^{2 <-- apply exponent rule; remove the multiplication asterisk}

5²(g⁵)²(h⁶)^{2 <-- take coefficient (5) out; prepare other exponents for multiplication}

5² = 25

(g⁵)² = g^5*2 = g¹⁰

(h⁶)² = h^6*2 = h^{12 <-- multiply the exponents for each variable}

25g¹⁰h^{12 <-- combine the results}

1. Repeat the same steps for the other half of the expression!

(g⁴ * h²)⁴

(g⁴h²)⁴

(g⁴)^{4 =} g^4*4 = g¹⁶

(h²)⁴ = h^2*4 = h⁸

g¹⁶h⁸

1. Now, to avoid getting confused, combine your expression back together, putting the same variables next to each other so that it is easier to look at.

25g¹⁰g¹⁶h¹²h^{8 <-- combined expression}

1. Next, you must add the exponents of the common variables together, following this format based off the exponent rule: a^ba^c = a^b+c

g¹⁰g¹⁶ = g¹⁰⁺¹⁶ = g^{26 <-- add g exponents together}

h¹²h⁸ = h¹²⁺⁸ = h^{20 <-- add h exponents together}

1. Finally, combine your final expression.

B. 25g²⁶ * h²⁰