Simplify the expression:

[tex]\[ \left(-5 g^2 h^6\right)^3 \][/tex]

A. [tex]\(-5 g^6 h^{18}\)[/tex]

B. [tex]\(125 g^6 h^{18}\)[/tex]

C. [tex]\(-125 g^6 h^{18}\)[/tex]

D. [tex]\(-125 g^5 h^9\)[/tex]



Answer :

To simplify the expression [tex]\(\left(-5 g^2 h^6\right)^3\)[/tex], we need to apply the rules of exponents:

1. Simplify the coefficient: We start with [tex]\(-5\)[/tex]. Raising [tex]\(-5\)[/tex] to the power of 3, we get [tex]\((-5)^3\)[/tex].

2. Simplify the exponent for [tex]\(g\)[/tex]: The original exponent on [tex]\(g\)[/tex] is 2. When raised to a power of 3, we multiply the exponents: [tex]\(2 \times 3\)[/tex].

3. Simplify the exponent for [tex]\(h\)[/tex]: The original exponent on [tex]\(h\)[/tex] is 6. When raised to a power of 3, we also multiply these exponents: [tex]\(6 \times 3\)[/tex].

Step-by-step:

1. Coefficient:
[tex]\[ (-5)^3 = -125 \][/tex]

2. Exponent for [tex]\(g\)[/tex]:
[tex]\[ (g^2)^3 = g^{2 \times 3} = g^6 \][/tex]

3. Exponent for [tex]\(h\)[/tex]:
[tex]\[ (h^6)^3 = h^{6 \times 3} = h^{18} \][/tex]

Putting it all together, the expression simplifies to:
[tex]\[ \left(-5 g^2 h^6\right)^3 = -125 g^6 h^{18} \][/tex]

Thus, the simplified expression is:
[tex]\[ -125 g^6 h^{18} \][/tex]

So, the correct answer is [tex]\(\boxed{-125 g^6 h^{18}}\)[/tex].